1# Montgomery Arithmetic; values are in the range [0, q). 2 3 4a = 00 5b = 00 6r = 00 7 8a = 00 9b = 01 10r = 01 11 12a = 00 13b = ffffffff00000001000000000000000000000000fffffffffffffffffffffffe 14r = ffffffff00000001000000000000000000000000fffffffffffffffffffffffe 15 16a = 01 17b = ffffffff00000001000000000000000000000000fffffffffffffffffffffffe 18r = 00 19 20a = 02 21b = ffffffff00000001000000000000000000000000fffffffffffffffffffffffe 22r = 01 23 24a = 03 25b = ffffffff00000001000000000000000000000000fffffffffffffffffffffffe 26r = 02 27 28a = 7fffffff800000008000000000000000000000007fffffffffffffffffffffff 29b = 7fffffff80000000800000000000000000000000800000000000000000000000 30r = 00 31 32a = 7fffffff80000000800000000000000000000000800000000000000000000000 33b = 7fffffff80000000800000000000000000000000800000000000000000000000 34r = 01 35 36a = 8000000000000000000000000000000000000000000000000000000000000000 37b = 8000000000000000000000000000000000000000000000000000000000000000 38r = fffffffeffffffffffffffffffffffff000000000000000000000001 39 40a = 8000000000000000000000000000000000000000000000000000000000000000 41b = 8000000000000000000000000000000000000000000000000000000000000000 42r = fffffffeffffffffffffffffffffffff000000000000000000000001 43 44a = 800000007fffffff7fffffffffffffffffffffff800000000000000000000001 45b = 7fffffff800000008000000000000000000000007fffffffffffffffffffffff 46r = fffffffeffffffffffffffffffffffff000000000000000000000001 47 48a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 49b = 8000000000000000000000000000000000000000000000000000000000000000 50r = fffffffeffffffffffffffffffffffff000000000000000000000000 51 52a = 800000007fffffff7fffffffffffffffffffffff800000000000000000000000 53b = 7fffffff800000008000000000000000000000007fffffffffffffffffffffff 54r = fffffffeffffffffffffffffffffffff000000000000000000000000 55 56# Carry Propagation. 57 58a = ff 59b = 01 60r = 0100 61 62a = 01ff 63b = 01 64r = 0200 65 66a = 03ff 67b = 01 68r = 0400 69 70a = 07ff 71b = 01 72r = 0800 73 74a = 0fff 75b = 01 76r = 1000 77 78a = 1fff 79b = 01 80r = 2000 81 82a = 3fff 83b = 01 84r = 4000 85 86a = 7fff 87b = 01 88r = 8000 89 90a = ffff 91b = 01 92r = 010000 93 94a = 01ffff 95b = 01 96r = 020000 97 98a = 03ffff 99b = 01 100r = 040000 101 102a = 07ffff 103b = 01 104r = 080000 105 106a = 0fffff 107b = 01 108r = 100000 109 110a = 1fffff 111b = 01 112r = 200000 113 114a = 3fffff 115b = 01 116r = 400000 117 118a = 7fffff 119b = 01 120r = 800000 121 122a = ffffff 123b = 01 124r = 01000000 125 126a = 01ffffff 127b = 01 128r = 02000000 129 130a = 03ffffff 131b = 01 132r = 04000000 133 134a = 07ffffff 135b = 01 136r = 08000000 137 138a = 0fffffff 139b = 01 140r = 10000000 141 142a = 1fffffff 143b = 01 144r = 20000000 145 146a = 3fffffff 147b = 01 148r = 40000000 149 150a = 7fffffff 151b = 01 152r = 80000000 153 154a = ffffffff 155b = 01 156r = 0100000000 157 158a = 01ffffffff 159b = 01 160r = 0200000000 161 162a = 03ffffffff 163b = 01 164r = 0400000000 165 166a = 07ffffffff 167b = 01 168r = 0800000000 169 170a = 0fffffffff 171b = 01 172r = 1000000000 173 174a = 1fffffffff 175b = 01 176r = 2000000000 177 178a = 3fffffffff 179b = 01 180r = 4000000000 181 182a = 7fffffffff 183b = 01 184r = 8000000000 185 186a = ffffffffff 187b = 01 188r = 010000000000 189 190a = 01ffffffffff 191b = 01 192r = 020000000000 193 194a = 03ffffffffff 195b = 01 196r = 040000000000 197 198a = 07ffffffffff 199b = 01 200r = 080000000000 201 202a = 0fffffffffff 203b = 01 204r = 100000000000 205 206a = 1fffffffffff 207b = 01 208r = 200000000000 209 210a = 3fffffffffff 211b = 01 212r = 400000000000 213 214a = 7fffffffffff 215b = 01 216r = 800000000000 217 218a = ffffffffffff 219b = 01 220r = 01000000000000 221 222a = 01ffffffffffff 223b = 01 224r = 02000000000000 225 226a = 03ffffffffffff 227b = 01 228r = 04000000000000 229 230a = 07ffffffffffff 231b = 01 232r = 08000000000000 233 234a = 0fffffffffffff 235b = 01 236r = 10000000000000 237 238a = 1fffffffffffff 239b = 01 240r = 20000000000000 241 242a = 3fffffffffffff 243b = 01 244r = 40000000000000 245 246a = 7fffffffffffff 247b = 01 248r = 80000000000000 249 250a = ffffffffffffff 251b = 01 252r = 0100000000000000 253 254a = 01ffffffffffffff 255b = 01 256r = 0200000000000000 257 258a = 03ffffffffffffff 259b = 01 260r = 0400000000000000 261 262a = 07ffffffffffffff 263b = 01 264r = 0800000000000000 265 266a = 0fffffffffffffff 267b = 01 268r = 1000000000000000 269 270a = 1fffffffffffffff 271b = 01 272r = 2000000000000000 273 274a = 3fffffffffffffff 275b = 01 276r = 4000000000000000 277 278a = 7fffffffffffffff 279b = 01 280r = 8000000000000000 281 282a = ffffffffffffffff 283b = 01 284r = 010000000000000000 285 286a = 01ffffffffffffffff 287b = 01 288r = 020000000000000000 289 290a = 03ffffffffffffffff 291b = 01 292r = 040000000000000000 293 294a = 07ffffffffffffffff 295b = 01 296r = 080000000000000000 297 298a = 0fffffffffffffffff 299b = 01 300r = 100000000000000000 301 302a = 1fffffffffffffffff 303b = 01 304r = 200000000000000000 305 306a = 3fffffffffffffffff 307b = 01 308r = 400000000000000000 309 310a = 7fffffffffffffffff 311b = 01 312r = 800000000000000000 313 314a = ffffffffffffffffff 315b = 01 316r = 01000000000000000000 317 318a = 01ffffffffffffffffff 319b = 01 320r = 02000000000000000000 321 322a = 03ffffffffffffffffff 323b = 01 324r = 04000000000000000000 325 326a = 07ffffffffffffffffff 327b = 01 328r = 08000000000000000000 329 330a = 0fffffffffffffffffff 331b = 01 332r = 10000000000000000000 333 334a = 1fffffffffffffffffff 335b = 01 336r = 20000000000000000000 337 338a = 3fffffffffffffffffff 339b = 01 340r = 40000000000000000000 341 342a = 7fffffffffffffffffff 343b = 01 344r = 80000000000000000000 345 346a = ffffffffffffffffffff 347b = 01 348r = 0100000000000000000000 349 350a = 01ffffffffffffffffffff 351b = 01 352r = 0200000000000000000000 353 354a = 03ffffffffffffffffffff 355b = 01 356r = 0400000000000000000000 357 358a = 07ffffffffffffffffffff 359b = 01 360r = 0800000000000000000000 361 362a = 0fffffffffffffffffffff 363b = 01 364r = 1000000000000000000000 365 366a = 1fffffffffffffffffffff 367b = 01 368r = 2000000000000000000000 369 370a = 3fffffffffffffffffffff 371b = 01 372r = 4000000000000000000000 373 374a = 7fffffffffffffffffffff 375b = 01 376r = 8000000000000000000000 377 378a = ffffffffffffffffffffff 379b = 01 380r = 010000000000000000000000 381 382a = 01ffffffffffffffffffffff 383b = 01 384r = 020000000000000000000000 385 386a = 03ffffffffffffffffffffff 387b = 01 388r = 040000000000000000000000 389 390a = 07ffffffffffffffffffffff 391b = 01 392r = 080000000000000000000000 393 394a = 0fffffffffffffffffffffff 395b = 01 396r = 100000000000000000000000 397 398a = 1fffffffffffffffffffffff 399b = 01 400r = 200000000000000000000000 401 402a = 3fffffffffffffffffffffff 403b = 01 404r = 400000000000000000000000 405 406a = 7fffffffffffffffffffffff 407b = 01 408r = 800000000000000000000000 409 410a = ffffffffffffffffffffffff 411b = 01 412r = 01000000000000000000000000 413 414a = 01ffffffffffffffffffffffff 415b = 01 416r = 02000000000000000000000000 417 418a = 03ffffffffffffffffffffffff 419b = 01 420r = 04000000000000000000000000 421 422a = 07ffffffffffffffffffffffff 423b = 01 424r = 08000000000000000000000000 425 426a = 0fffffffffffffffffffffffff 427b = 01 428r = 10000000000000000000000000 429 430a = 1fffffffffffffffffffffffff 431b = 01 432r = 20000000000000000000000000 433 434a = 3fffffffffffffffffffffffff 435b = 01 436r = 40000000000000000000000000 437 438a = 7fffffffffffffffffffffffff 439b = 01 440r = 80000000000000000000000000 441 442a = ffffffffffffffffffffffffff 443b = 01 444r = 0100000000000000000000000000 445 446a = 01ffffffffffffffffffffffffff 447b = 01 448r = 0200000000000000000000000000 449 450a = 03ffffffffffffffffffffffffff 451b = 01 452r = 0400000000000000000000000000 453 454a = 07ffffffffffffffffffffffffff 455b = 01 456r = 0800000000000000000000000000 457 458a = 0fffffffffffffffffffffffffff 459b = 01 460r = 1000000000000000000000000000 461 462a = 1fffffffffffffffffffffffffff 463b = 01 464r = 2000000000000000000000000000 465 466a = 3fffffffffffffffffffffffffff 467b = 01 468r = 4000000000000000000000000000 469 470a = 7fffffffffffffffffffffffffff 471b = 01 472r = 8000000000000000000000000000 473 474a = ffffffffffffffffffffffffffff 475b = 01 476r = 010000000000000000000000000000 477 478a = 01ffffffffffffffffffffffffffff 479b = 01 480r = 020000000000000000000000000000 481 482a = 03ffffffffffffffffffffffffffff 483b = 01 484r = 040000000000000000000000000000 485 486a = 07ffffffffffffffffffffffffffff 487b = 01 488r = 080000000000000000000000000000 489 490a = 0fffffffffffffffffffffffffffff 491b = 01 492r = 100000000000000000000000000000 493 494a = 1fffffffffffffffffffffffffffff 495b = 01 496r = 200000000000000000000000000000 497 498a = 3fffffffffffffffffffffffffffff 499b = 01 500r = 400000000000000000000000000000 501 502a = 7fffffffffffffffffffffffffffff 503b = 01 504r = 800000000000000000000000000000 505 506a = ffffffffffffffffffffffffffffff 507b = 01 508r = 01000000000000000000000000000000 509 510a = 01ffffffffffffffffffffffffffffff 511b = 01 512r = 02000000000000000000000000000000 513 514a = 03ffffffffffffffffffffffffffffff 515b = 01 516r = 04000000000000000000000000000000 517 518a = 07ffffffffffffffffffffffffffffff 519b = 01 520r = 08000000000000000000000000000000 521 522a = 0fffffffffffffffffffffffffffffff 523b = 01 524r = 10000000000000000000000000000000 525 526a = 1fffffffffffffffffffffffffffffff 527b = 01 528r = 20000000000000000000000000000000 529 530a = 3fffffffffffffffffffffffffffffff 531b = 01 532r = 40000000000000000000000000000000 533 534a = 7fffffffffffffffffffffffffffffff 535b = 01 536r = 80000000000000000000000000000000 537 538a = ffffffffffffffffffffffffffffffff 539b = 01 540r = 0100000000000000000000000000000000 541 542a = 01ffffffffffffffffffffffffffffffff 543b = 01 544r = 0200000000000000000000000000000000 545 546a = 03ffffffffffffffffffffffffffffffff 547b = 01 548r = 0400000000000000000000000000000000 549 550a = 07ffffffffffffffffffffffffffffffff 551b = 01 552r = 0800000000000000000000000000000000 553 554a = 0fffffffffffffffffffffffffffffffff 555b = 01 556r = 1000000000000000000000000000000000 557 558a = 1fffffffffffffffffffffffffffffffff 559b = 01 560r = 2000000000000000000000000000000000 561 562a = 3fffffffffffffffffffffffffffffffff 563b = 01 564r = 4000000000000000000000000000000000 565 566a = 7fffffffffffffffffffffffffffffffff 567b = 01 568r = 8000000000000000000000000000000000 569 570a = ffffffffffffffffffffffffffffffffff 571b = 01 572r = 010000000000000000000000000000000000 573 574a = 01ffffffffffffffffffffffffffffffffff 575b = 01 576r = 020000000000000000000000000000000000 577 578a = 03ffffffffffffffffffffffffffffffffff 579b = 01 580r = 040000000000000000000000000000000000 581 582a = 07ffffffffffffffffffffffffffffffffff 583b = 01 584r = 080000000000000000000000000000000000 585 586a = 0fffffffffffffffffffffffffffffffffff 587b = 01 588r = 100000000000000000000000000000000000 589 590a = 1fffffffffffffffffffffffffffffffffff 591b = 01 592r = 200000000000000000000000000000000000 593 594a = 3fffffffffffffffffffffffffffffffffff 595b = 01 596r = 400000000000000000000000000000000000 597 598a = 7fffffffffffffffffffffffffffffffffff 599b = 01 600r = 800000000000000000000000000000000000 601 602a = ffffffffffffffffffffffffffffffffffff 603b = 01 604r = 01000000000000000000000000000000000000 605 606a = 01ffffffffffffffffffffffffffffffffffff 607b = 01 608r = 02000000000000000000000000000000000000 609 610a = 03ffffffffffffffffffffffffffffffffffff 611b = 01 612r = 04000000000000000000000000000000000000 613 614a = 07ffffffffffffffffffffffffffffffffffff 615b = 01 616r = 08000000000000000000000000000000000000 617 618a = 0fffffffffffffffffffffffffffffffffffff 619b = 01 620r = 10000000000000000000000000000000000000 621 622a = 1fffffffffffffffffffffffffffffffffffff 623b = 01 624r = 20000000000000000000000000000000000000 625 626a = 3fffffffffffffffffffffffffffffffffffff 627b = 01 628r = 40000000000000000000000000000000000000 629 630a = 7fffffffffffffffffffffffffffffffffffff 631b = 01 632r = 80000000000000000000000000000000000000 633 634a = ffffffffffffffffffffffffffffffffffffff 635b = 01 636r = 0100000000000000000000000000000000000000 637 638a = 01ffffffffffffffffffffffffffffffffffffff 639b = 01 640r = 0200000000000000000000000000000000000000 641 642a = 03ffffffffffffffffffffffffffffffffffffff 643b = 01 644r = 0400000000000000000000000000000000000000 645 646a = 07ffffffffffffffffffffffffffffffffffffff 647b = 01 648r = 0800000000000000000000000000000000000000 649 650a = 0fffffffffffffffffffffffffffffffffffffff 651b = 01 652r = 1000000000000000000000000000000000000000 653 654a = 1fffffffffffffffffffffffffffffffffffffff 655b = 01 656r = 2000000000000000000000000000000000000000 657 658a = 3fffffffffffffffffffffffffffffffffffffff 659b = 01 660r = 4000000000000000000000000000000000000000 661 662a = 7fffffffffffffffffffffffffffffffffffffff 663b = 01 664r = 8000000000000000000000000000000000000000 665 666a = ffffffffffffffffffffffffffffffffffffffff 667b = 01 668r = 010000000000000000000000000000000000000000 669 670a = 01ffffffffffffffffffffffffffffffffffffffff 671b = 01 672r = 020000000000000000000000000000000000000000 673 674a = 03ffffffffffffffffffffffffffffffffffffffff 675b = 01 676r = 040000000000000000000000000000000000000000 677 678a = 07ffffffffffffffffffffffffffffffffffffffff 679b = 01 680r = 080000000000000000000000000000000000000000 681 682a = 0fffffffffffffffffffffffffffffffffffffffff 683b = 01 684r = 100000000000000000000000000000000000000000 685 686a = 1fffffffffffffffffffffffffffffffffffffffff 687b = 01 688r = 200000000000000000000000000000000000000000 689 690a = 3fffffffffffffffffffffffffffffffffffffffff 691b = 01 692r = 400000000000000000000000000000000000000000 693 694a = 7fffffffffffffffffffffffffffffffffffffffff 695b = 01 696r = 800000000000000000000000000000000000000000 697 698a = ffffffffffffffffffffffffffffffffffffffffff 699b = 01 700r = 01000000000000000000000000000000000000000000 701 702a = 01ffffffffffffffffffffffffffffffffffffffffff 703b = 01 704r = 02000000000000000000000000000000000000000000 705 706a = 03ffffffffffffffffffffffffffffffffffffffffff 707b = 01 708r = 04000000000000000000000000000000000000000000 709 710a = 07ffffffffffffffffffffffffffffffffffffffffff 711b = 01 712r = 08000000000000000000000000000000000000000000 713 714a = 0fffffffffffffffffffffffffffffffffffffffffff 715b = 01 716r = 10000000000000000000000000000000000000000000 717 718a = 1fffffffffffffffffffffffffffffffffffffffffff 719b = 01 720r = 20000000000000000000000000000000000000000000 721 722a = 3fffffffffffffffffffffffffffffffffffffffffff 723b = 01 724r = 40000000000000000000000000000000000000000000 725 726a = 7fffffffffffffffffffffffffffffffffffffffffff 727b = 01 728r = 80000000000000000000000000000000000000000000 729 730a = ffffffffffffffffffffffffffffffffffffffffffff 731b = 01 732r = 0100000000000000000000000000000000000000000000 733 734a = 01ffffffffffffffffffffffffffffffffffffffffffff 735b = 01 736r = 0200000000000000000000000000000000000000000000 737 738a = 03ffffffffffffffffffffffffffffffffffffffffffff 739b = 01 740r = 0400000000000000000000000000000000000000000000 741 742a = 07ffffffffffffffffffffffffffffffffffffffffffff 743b = 01 744r = 0800000000000000000000000000000000000000000000 745 746a = 0fffffffffffffffffffffffffffffffffffffffffffff 747b = 01 748r = 1000000000000000000000000000000000000000000000 749 750a = 1fffffffffffffffffffffffffffffffffffffffffffff 751b = 01 752r = 2000000000000000000000000000000000000000000000 753 754a = 3fffffffffffffffffffffffffffffffffffffffffffff 755b = 01 756r = 4000000000000000000000000000000000000000000000 757 758a = 7fffffffffffffffffffffffffffffffffffffffffffff 759b = 01 760r = 8000000000000000000000000000000000000000000000 761 762a = ffffffffffffffffffffffffffffffffffffffffffffff 763b = 01 764r = 010000000000000000000000000000000000000000000000 765 766a = 01ffffffffffffffffffffffffffffffffffffffffffffff 767b = 01 768r = 020000000000000000000000000000000000000000000000 769 770a = 03ffffffffffffffffffffffffffffffffffffffffffffff 771b = 01 772r = 040000000000000000000000000000000000000000000000 773 774a = 07ffffffffffffffffffffffffffffffffffffffffffffff 775b = 01 776r = 080000000000000000000000000000000000000000000000 777 778a = 0fffffffffffffffffffffffffffffffffffffffffffffff 779b = 01 780r = 100000000000000000000000000000000000000000000000 781 782a = 1fffffffffffffffffffffffffffffffffffffffffffffff 783b = 01 784r = 200000000000000000000000000000000000000000000000 785 786a = 3fffffffffffffffffffffffffffffffffffffffffffffff 787b = 01 788r = 400000000000000000000000000000000000000000000000 789 790a = 7fffffffffffffffffffffffffffffffffffffffffffffff 791b = 01 792r = 800000000000000000000000000000000000000000000000 793 794a = ffffffffffffffffffffffffffffffffffffffffffffffff 795b = 01 796r = 01000000000000000000000000000000000000000000000000 797 798a = 01ffffffffffffffffffffffffffffffffffffffffffffffff 799b = 01 800r = 02000000000000000000000000000000000000000000000000 801 802a = 03ffffffffffffffffffffffffffffffffffffffffffffffff 803b = 01 804r = 04000000000000000000000000000000000000000000000000 805 806a = 07ffffffffffffffffffffffffffffffffffffffffffffffff 807b = 01 808r = 08000000000000000000000000000000000000000000000000 809 810a = 0fffffffffffffffffffffffffffffffffffffffffffffffff 811b = 01 812r = 10000000000000000000000000000000000000000000000000 813 814a = 1fffffffffffffffffffffffffffffffffffffffffffffffff 815b = 01 816r = 20000000000000000000000000000000000000000000000000 817 818a = 3fffffffffffffffffffffffffffffffffffffffffffffffff 819b = 01 820r = 40000000000000000000000000000000000000000000000000 821 822a = 7fffffffffffffffffffffffffffffffffffffffffffffffff 823b = 01 824r = 80000000000000000000000000000000000000000000000000 825 826a = ffffffffffffffffffffffffffffffffffffffffffffffffff 827b = 01 828r = 0100000000000000000000000000000000000000000000000000 829 830a = 01ffffffffffffffffffffffffffffffffffffffffffffffffff 831b = 01 832r = 0200000000000000000000000000000000000000000000000000 833 834a = 03ffffffffffffffffffffffffffffffffffffffffffffffffff 835b = 01 836r = 0400000000000000000000000000000000000000000000000000 837 838a = 07ffffffffffffffffffffffffffffffffffffffffffffffffff 839b = 01 840r = 0800000000000000000000000000000000000000000000000000 841 842a = 0fffffffffffffffffffffffffffffffffffffffffffffffffff 843b = 01 844r = 1000000000000000000000000000000000000000000000000000 845 846a = 1fffffffffffffffffffffffffffffffffffffffffffffffffff 847b = 01 848r = 2000000000000000000000000000000000000000000000000000 849 850a = 3fffffffffffffffffffffffffffffffffffffffffffffffffff 851b = 01 852r = 4000000000000000000000000000000000000000000000000000 853 854a = 7fffffffffffffffffffffffffffffffffffffffffffffffffff 855b = 01 856r = 8000000000000000000000000000000000000000000000000000 857 858a = ffffffffffffffffffffffffffffffffffffffffffffffffffff 859b = 01 860r = 010000000000000000000000000000000000000000000000000000 861 862a = 01ffffffffffffffffffffffffffffffffffffffffffffffffffff 863b = 01 864r = 020000000000000000000000000000000000000000000000000000 865 866a = 03ffffffffffffffffffffffffffffffffffffffffffffffffffff 867b = 01 868r = 040000000000000000000000000000000000000000000000000000 869 870a = 07ffffffffffffffffffffffffffffffffffffffffffffffffffff 871b = 01 872r = 080000000000000000000000000000000000000000000000000000 873 874a = 0fffffffffffffffffffffffffffffffffffffffffffffffffffff 875b = 01 876r = 100000000000000000000000000000000000000000000000000000 877 878a = 1fffffffffffffffffffffffffffffffffffffffffffffffffffff 879b = 01 880r = 200000000000000000000000000000000000000000000000000000 881 882a = 3fffffffffffffffffffffffffffffffffffffffffffffffffffff 883b = 01 884r = 400000000000000000000000000000000000000000000000000000 885 886a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffff 887b = 01 888r = 800000000000000000000000000000000000000000000000000000 889 890a = ffffffffffffffffffffffffffffffffffffffffffffffffffffff 891b = 01 892r = 01000000000000000000000000000000000000000000000000000000 893 894a = 01ffffffffffffffffffffffffffffffffffffffffffffffffffffff 895b = 01 896r = 02000000000000000000000000000000000000000000000000000000 897 898a = 03ffffffffffffffffffffffffffffffffffffffffffffffffffffff 899b = 01 900r = 04000000000000000000000000000000000000000000000000000000 901 902a = 07ffffffffffffffffffffffffffffffffffffffffffffffffffffff 903b = 01 904r = 08000000000000000000000000000000000000000000000000000000 905 906a = 0fffffffffffffffffffffffffffffffffffffffffffffffffffffff 907b = 01 908r = 10000000000000000000000000000000000000000000000000000000 909 910a = 1fffffffffffffffffffffffffffffffffffffffffffffffffffffff 911b = 01 912r = 20000000000000000000000000000000000000000000000000000000 913 914a = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffff 915b = 01 916r = 40000000000000000000000000000000000000000000000000000000 917 918a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffffff 919b = 01 920r = 80000000000000000000000000000000000000000000000000000000 921 922a = ffffffffffffffffffffffffffffffffffffffffffffffffffffffff 923b = 01 924r = 0100000000000000000000000000000000000000000000000000000000 925 926a = 01ffffffffffffffffffffffffffffffffffffffffffffffffffffffff 927b = 01 928r = 0200000000000000000000000000000000000000000000000000000000 929 930a = 03ffffffffffffffffffffffffffffffffffffffffffffffffffffffff 931b = 01 932r = 0400000000000000000000000000000000000000000000000000000000 933 934a = 07ffffffffffffffffffffffffffffffffffffffffffffffffffffffff 935b = 01 936r = 0800000000000000000000000000000000000000000000000000000000 937 938a = 0fffffffffffffffffffffffffffffffffffffffffffffffffffffffff 939b = 01 940r = 1000000000000000000000000000000000000000000000000000000000 941 942a = 1fffffffffffffffffffffffffffffffffffffffffffffffffffffffff 943b = 01 944r = 2000000000000000000000000000000000000000000000000000000000 945 946a = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffff 947b = 01 948r = 4000000000000000000000000000000000000000000000000000000000 949 950a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffffffff 951b = 01 952r = 8000000000000000000000000000000000000000000000000000000000 953 954a = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 955b = 01 956r = 010000000000000000000000000000000000000000000000000000000000 957 958a = 01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 959b = 01 960r = 020000000000000000000000000000000000000000000000000000000000 961 962a = 03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 963b = 01 964r = 040000000000000000000000000000000000000000000000000000000000 965 966a = 07ffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 967b = 01 968r = 080000000000000000000000000000000000000000000000000000000000 969 970a = 0fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 971b = 01 972r = 100000000000000000000000000000000000000000000000000000000000 973 974a = 1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 975b = 01 976r = 200000000000000000000000000000000000000000000000000000000000 977 978a = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 979b = 01 980r = 400000000000000000000000000000000000000000000000000000000000 981 982a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 983b = 01 984r = 800000000000000000000000000000000000000000000000000000000000 985 986a = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 987b = 01 988r = 01000000000000000000000000000000000000000000000000000000000000 989 990a = 01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 991b = 01 992r = 02000000000000000000000000000000000000000000000000000000000000 993 994a = 03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 995b = 01 996r = 04000000000000000000000000000000000000000000000000000000000000 997 998a = 07ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 999b = 01 1000r = 08000000000000000000000000000000000000000000000000000000000000 1001 1002a = 0fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1003b = 01 1004r = 10000000000000000000000000000000000000000000000000000000000000 1005 1006a = 1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1007b = 01 1008r = 20000000000000000000000000000000000000000000000000000000000000 1009 1010a = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1011b = 01 1012r = 40000000000000000000000000000000000000000000000000000000000000 1013 1014a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1015b = 01 1016r = 80000000000000000000000000000000000000000000000000000000000000 1017 1018a = ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1019b = 01 1020r = 0100000000000000000000000000000000000000000000000000000000000000 1021 1022a = 01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1023b = 01 1024r = 0200000000000000000000000000000000000000000000000000000000000000 1025 1026a = 03ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1027b = 01 1028r = 0400000000000000000000000000000000000000000000000000000000000000 1029 1030a = 07ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1031b = 01 1032r = 0800000000000000000000000000000000000000000000000000000000000000 1033 1034a = 0fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1035b = 01 1036r = 1000000000000000000000000000000000000000000000000000000000000000 1037 1038a = 1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1039b = 01 1040r = 2000000000000000000000000000000000000000000000000000000000000000 1041 1042a = 3fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1043b = 01 1044r = 4000000000000000000000000000000000000000000000000000000000000000 1045 1046a = 7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff 1047b = 01 1048r = 8000000000000000000000000000000000000000000000000000000000000000 1049