b := (1,2029,2058)( 2,  80, 608)(   3,1971,1803)(   4, 422, 649)
(   5,1059,1889)(   6,1730, 276)(   7,1615,2186)(   8, 375,1414)
(   9,2015,1513)(  10, 541, 832)(  11,2148,1598)(  12,1181,1067)
(  13, 416,  95)(  14, 117, 119)(  15,2132, 438)(  16, 468, 897)
(  17,1653,1807)(  18,1158, 634)(  19,1719, 520)(  20, 550,2165)
(  21,1029, 491)(  22,1931, 993)(  23, 984,1953)(  24, 118,1610)
(  25,1549, 457)(  26, 138, 840)(  27,1368,1522)(  28, 424,1939)
(  29,1455,1624)(  30, 909, 573)(  31,  42,1173)(  32, 655,1617)
(  33, 184, 323)(  34,1535,1637)(  35,1215, 155)(  36,1954, 883)
(  37, 937,1713)(  38,  66,2100)(  39,1401,1261)(  40,2107,2156)
(  41, 934,1411)(  43,1676,1502)(  44,1454,1508)(  45, 795,1922)
(  46,1633,1853)(  47,1664, 261)(  48, 336, 501)(  49, 135, 306)
(  50,  76, 356)(  51,2144, 494)(  52,1655,1034)(  53,1723,1556)
(  54,1928,1710)(  55,1743, 440)(  56,1861, 874)(  57,1930,1815)
(  58, 714,1272)(  59,2046,1826)(  60,2096,2055)(  61,1281,1344)
(  62,1209,2177)(  63,1429, 733)(  64,1635,2001)(  65, 163,1052)
(  67,1829,1050)(  68,1399,1649)(  69,2127, 570)(  70,  99, 434)
(  71, 814,1060)(  72, 556,2125)(  73,1066,1705)(  74,1366, 209)
(  75,1457,1704)(  77,1520,1416)(  78,1303,1852)(  79,1895, 345)
(  81,1691, 269)(  82,1230,  94)(  83,1916, 299)(  84,1221,1541)
(  85, 710,1081)(  86,1500, 586)(  87,2102, 137)(  88, 397, 652)
(  89,1019,1423)(  90,1146,1941)(  91, 815,1618)(  92, 287,1997)
(  93,2169, 680)(  96, 966,2051)(  97,1503,1165)(  98,1219, 701)
( 100,1144,1732)( 101, 631,1276)( 102, 533, 258)( 103, 327,1837)
( 104, 709,1224)( 105, 612,2183)( 106, 778, 768)( 107,1570,1334)
( 108,1951,1122)( 109, 899, 730)( 110, 737,1126)( 111, 975,1918)
( 112, 589, 976)( 113,1367,1949)( 114, 726, 263)( 115, 919, 201)
( 116,1420, 172)( 120,1660, 560)( 121,2028, 914)( 122, 978,1238)
( 123,1739, 419)( 124,1868,1084)( 125,1510, 333)( 126,1741, 801)
( 127,1902,1217)( 128, 656,1469)( 129,1470,1813)( 130, 412,1888)
( 131, 304,2038)( 132,1711,1693)( 133, 311, 509)( 134, 389,1475)
( 136, 400,1415)( 139,1785, 439)( 140,1948,1860)( 141,1495,1379)
( 142,1507, 886)( 143, 943, 807)( 144,1094,2116)( 145, 256, 315)
( 146,1382,1337)( 147,1190,2082)( 148,1952,2195)( 149, 179, 563)
( 150, 866,2194)( 151, 820, 678)( 152, 896,2087)( 153,1212, 803)
( 154, 313,1160)( 156,1798, 770)( 157,1762,1782)( 158, 689,1232)
( 159,1913,2077)( 160,1208,1132)( 161, 534,1145)( 162, 702,1740)
( 164,1451,1531)( 165, 844,1127)( 166, 568, 838)( 167, 484,1968)
( 168, 232, 300)( 169, 510,1594)( 170,1474, 920)( 171,1498,1325)
( 173, 970,1554)( 174, 283, 208)( 175,1804,1555)( 176,1064,2103)
( 177, 594, 188)( 178, 780,1712)( 180, 640, 956)( 181, 444, 585)
( 182,1816,1135)( 183,1793,1119)( 185, 517,1851)( 186,1683, 788)
( 187, 769, 341)( 189,1256,1157)( 190, 607, 688)( 191,2092,1105)
( 192,1694, 551)( 193, 907, 715)( 194, 406, 301)( 195,1372,1077)
( 196,1628,2112)( 197,2036,1747)( 198,1188, 718)( 199, 289,2080)
( 200, 282, 624)( 202,1688,1792)( 203,1263, 641)( 204,1657, 495)
( 205, 380, 273)( 206,1509,2171)( 207, 388, 482)( 210, 360, 661)
( 211, 512,1871)( 212, 854, 629)( 213,1577, 824)( 214,1882,1724)
( 215, 698,1487)( 216, 476, 881)( 217,2061, 334)( 218, 960, 364)
( 219,1193,1822)( 220,1992,1452)( 221,1945,1101)( 222,1100, 998)
( 223, 690, 662)( 224, 564, 979)( 225,1830, 587)( 226, 772, 508)
( 227,1023,1566)( 228,1384, 750)( 229,1855, 480)( 230, 293,1848)
( 231, 925, 946)( 233,1318, 277)( 234, 848,1982)( 235,1987,2002)
( 236, 248,2065)( 237, 339,1191)( 238, 872,1155)( 239,1257,1290)
( 240, 924,2035)( 241,1544,1770)( 242,1421,2053)( 243,1274, 618)
( 244, 295,2041)( 245,1298, 481)( 246,1151, 994)( 247,2197,1659)
( 249,1828, 906)( 250, 297,1590)( 251, 623,1063)( 252,1838,1760)
( 253,1909, 347)( 254, 630, 453)( 255, 274, 983)( 257, 974, 506)
( 259, 996,2007)( 260, 779, 796)( 262,1116, 450)( 264,1870, 553)
( 265, 643, 384)( 266,1536,1014)( 267, 358,2031)( 268, 543,1348)
( 270, 598, 787)( 271, 381, 596)( 272, 679,1731)( 275, 948,1658)
( 278,2011,1073)( 279, 947,1226)( 280,1698,1134)( 281,1820,2160)
( 284,1061,1647)( 285,1330,1512)( 286,1494, 359)( 288,1310,1593)
( 290,2182,1970)( 291, 436,1068)( 292,1975, 519)( 294, 314, 637)
( 296,1085, 635)( 298, 671,1501)( 302, 805, 460)( 303,1835, 681)
( 305,1900,1291)( 307, 357, 407)( 308,1117,1499)( 309, 827, 392)
( 310, 940,1840)( 312,1742, 692)( 316,1591,1453)( 317, 684,1016)
( 318,1030, 771)( 319,1518,1444)( 320,1461, 957)( 321,1858,1958)
( 322,1879,1985)( 324,1252,1231)( 325, 766,1302)( 326,2085,2032)
( 328, 835, 686)( 329,1207,1716)( 330, 990,1412)( 331, 703,2047)
( 332,1079,1205)( 335, 808,1072)( 337, 930,1024)( 338, 911,1936)
( 340,1011,1990)( 342,1137,1371)( 343,1682,1182)( 344,1771,1168)
( 346,1548,1725)( 348,1559,1642)( 349, 761,1715)( 350,1464,1478)
( 351,1675,1619)( 352,1069,2024)( 353, 884,1684)( 354, 955, 669)
( 355, 794,1944)( 361,2188, 721)( 362,1532,1259)( 363,2167, 455)
( 365, 888, 485)( 366, 469, 870)( 367, 537, 666)( 368,1326,1906)
( 369,1167, 429)( 370,1491,1625)( 371,1409,1961)( 372,1910, 817)
( 373,1433, 812)( 374,1428,2104)( 376,1317,1333)( 377,1606, 617)
( 378,1301, 488)( 379,1228, 549)( 382,1527,1687)( 383, 968,2189)
( 385,1434,1825)( 386, 578, 887)( 387,1242, 773)( 390,1581, 860)
( 391,1311,1049)( 393, 851,1927)( 394,1925,1673)( 395,1588,1867)
( 396,1702, 802)( 398,1218, 836)( 399, 767, 442)( 401,1864,1769)
( 402, 729,1128)( 403, 660,1377)( 404,1784,1875)( 405,2059,1314)
( 408, 674,1435)( 409,1582,1646)( 410,1046,1695)( 411,1268, 486)
( 413,2063, 790)( 414,2090, 743)( 415,1456, 871)( 417, 744,1506)
( 418, 792,1609)( 420,1035, 826)( 421,1351,1388)( 423, 895,1465)
( 425, 931, 892)( 426,1288,1436)( 427,2121,1468)( 428,1914, 935)
( 430,1737,2166)( 431,1753,1613)( 432,1375,2159)( 433, 736,1407)
( 435,1643, 727)( 437, 524,1031)( 441, 891,1674)( 443, 819,1841)
( 445,1391,1267)( 446,2153,1748)( 447,1645, 528)( 448,2170,1876)
( 449, 999,2027)( 451,1480,1010)( 452,1539,1872)( 454, 530,1877)
( 456,1442,1439)( 458,1526,1553)( 459,1080, 719)( 461, 590,1074)
( 462, 763,2145)( 463,1994,1053)( 464, 527,1641)( 465, 982,2154)
( 466,1162, 745)( 467,1343, 905)( 470,1511, 536)( 471, 856,1103)
( 472,1427,1666)( 473,2016,2191)( 474,1981,1565)( 475,1797,1057)
( 477,1269,1143)( 478, 786, 622)( 479,1557,1328)( 483, 627, 645)
( 487,1092, 923)( 489,1460,1009)( 490, 845,1448)( 492,1616,1632)
( 493,1812, 514)( 496,2025, 735)( 497,1323, 621)( 498,1083,2118)
( 499,1331,1996)( 500,1446, 646)( 502,1021, 673)( 503,2158,1787)
( 504, 526, 941)( 505,1295,1486)( 507,1993, 843)( 511,1777,1202)
( 513,2017,1640)( 515,1204,1042)( 516,1690,1027)( 518,1767,1650)
( 521,1667, 852)( 522,1233,1920)( 523,2192, 958)( 525, 683,1490)
( 529,2176,1481)( 531,2136,2162)( 532,1834,1036)( 535,2149,1007)
( 538,1152,1529)( 539, 555,2042)( 540,1950, 781)( 542,2069,1284)
( 544,1865, 638)( 545,1668, 849)( 546,1669,1299)( 547,2134, 764)
( 548, 882,2184)( 552, 921,1721)( 554,1969,1365)( 557, 755,1033)
( 558,1362,1201)( 559,1884, 591)( 561,1589, 963)( 562,1347,2196)
( 565,1778,1346)( 566, 833,1449)( 567, 722,1223)( 569, 633,2114)
( 571,1597,1319)( 572,1818,1957)( 574, 942,1345)( 575,1142, 904)
( 576, 829, 950)( 577,2155,2088)( 579, 785,1773)( 580, 667,2056)
( 581,1735,1109)( 582, 783, 971)( 583,1241,1153)( 584,1964,2022)
( 588, 620,1626)( 592,1255,1978)( 593,1471,1189)( 595,1342,2049)
( 597,2187,1431)( 599,1194, 972)( 600, 657, 670)( 601,1148, 665)
( 602,1989,1447)( 603,1542, 734)( 604,1756,1195)( 605,2044, 711)
( 606, 784, 912)( 609,1839,1363)( 610,1986,1786)( 611,1206, 654)
( 613, 902,1670)( 614,2111,1738)( 615,1775,1576)( 616,2070,1998)
( 619,1293,1862)( 625,2142,1297)( 626,1672,1586)( 628,1493, 811)
( 632,1025,1349)( 636,2040, 839)( 639,1592, 876)( 642,2193, 651)
( 644, 967, 877)( 647,1140,1585)( 648,1260,2052)( 653,2099, 927)
( 658,2094,1150)( 659,2034, 959)( 663,2122,1192)( 664,1138,1962)
( 668,1538,1424)( 672,2161, 828)( 675,1663,2117)( 676,1104,1842)
( 677,1708,2101)( 682,1504,1017)( 685,1976,2175)( 687, 753,2013)
( 691,1661, 696)( 693,1185,1977)( 694,1866,1289)( 695,1108,1934)
( 697,1772, 818)( 699, 777,1781)( 700, 746,1685)( 704, 900,1149)
( 705, 797, 981)( 706, 804,1315)( 707,1236,2039)( 708,1369,2068)
( 712, 731,1524)( 713,1898,1933)( 716,1572,1886)( 717,2168,1697)
( 720,1111,2180)( 723,1051,1608)( 724,1225,1292)( 725,1824,1550)
( 728, 936,1106)( 732,1139,2135)( 738,2075,1216)( 739,1648,1899)
( 740, 995,2074)( 741,1701,1249)( 742,2000, 859)( 747,1118,2185)
( 748,1322, 988)( 749, 847,1942)( 751,1197, 964)( 752,1203,1679)
( 754, 908,1800)( 756,1078,1863)( 757,2172,1759)( 758,2130,1047)
( 759,2120,1623)( 760, 945,1521)( 762,1736,2084)( 765,1894,1780)
( 774,1983,1054)( 775,1186,1244)( 776,1040,1418)( 782,1169,1744)
( 789,1321,1707)( 791,2179,1370)( 793,2023,1045)( 798,2113,1183)
( 799,2050,1056)( 800,1946,1973)( 806,1573,1755)( 809,2119,1214)
( 810,1564,1620)( 813,1497, 913)( 816,1199,1361)( 821,1689, 928)
( 822,2178,1359)( 823,1530,1897)( 825,2133,1754)( 830,2004,1121)
( 831,1599, 961)( 834,1038,1120)( 837,1166,1383)( 841,1571, 929)
( 842,1703,1846)( 846,1718,1039)( 850,1028,1700)( 853,1176,1385)
( 855, 992,1058)( 857,1001,1605)( 858,1639,1438)( 861,1254,1965)
( 862,1847,1774)( 863,1022,1277)( 864,1561,1397)( 865,1546,1258)
( 867,1567,1917)( 868,1854,2137)( 869,1124,1467)( 873, 894,1280)
( 875,1802,1432)( 878,1569,2163)( 879,1400,1856)( 880,1309,1602)
( 885,1887,2091)( 889,2064,1540)( 890,1012,1265)( 893, 986,1796)
( 898,1013,1005)( 901,1341,1943)( 903, 952,1514)( 910, 944,2173)
( 915,1187,1595)( 916,1578,1483)( 917,2057,1584)( 918,1308,1809)
( 922,1537,1776)( 926,1450,1677)( 932,1141,1831)( 933,1603,1220)
( 938,1283,1956)( 939,2115,2026)( 949,1032,1099)( 951, 969,1799)
( 953,1533,1612)( 954,1859,1534)( 962,1960,2097)( 965,1728,1751)
( 973,2048,2147)( 977,1709, 985)( 980,1294,1893)( 987,1779,2139)
( 989,2009,1477)( 991,2043,2164)( 997,1086,2005)(1000,1115,1908)
(1002,1222,1210)(1003,1891,1967)(1004,1795,2083)(1006,1980,1622)
(1008,1600,1093)(1015,1814,1699)(1018,1849,1282)(1020,1935,2045)
(1026,2060,2010)(1037,1912,1551)(1041,1107,1806)(1043,1250,1243)
(1044,2089,1445)(1048,1320,1915)(1055,1733,1517)(1062,1376,1463)
(1065,1076,2066)(1070,1883,1880)(1071,2033,1170)(1075,1720,1966)
(1082,2071,1717)(1087,2012,2141)(1088,1262,1801)(1089,1458,1307)
(1090,1631,1180)(1091,1519,1680)(1095,1279,1395)(1096,1147,1245)
(1097,1246,1516)(1098,2190,1845)(1102,1757,2108)(1110,1358,1306)
(1112,1154,1638)(1113,1248,1523)(1114,1791,1974)(1123,1543,1178)
(1125,1355,1386)(1129,2181,1808)(1130,1505,1211)(1131,1247,1545)
(1133,1904,1275)(1136,1568,1794)(1156,1417,1378)(1159,1380,1402)
(1161,1850,2138)(1163,1750,1316)(1164,2078,1885)(1171,2079,2072)
(1172,2098,1492)(1174,2037,1394)(1175,1903,1227)(1177,1901,1552)
(1179,1790,1515)(1184,1601,1627)(1196,1805,1832)(1198,1656,1706)
(1200,1819,2062)(1213,1749,1766)(1229,1634,1843)(1234,1329,1644)
(1235,1440,1919)(1237,1528,2110)(1239,1869,1810)(1240,1285,1823)
(1251,1304,1607)(1253,1286,1406)(1264,1443,1392)(1266,1583,1729)
(1270,1696,2105)(1271,1984,1396)(1273,1636,2150)(1278,1844,1357)
(1287,1339,1921)(1296,1482,1692)(1300,1459,1413)(1305,1580,1671)
(1312,1354,2152)(1313,1614,2129)(1324,1734,1563)(1327,1560,1579)
(1332,1340,1654)(1335,1364,1437)(1336,1488,1360)(1338,1353,1959)
(1350,1874,2143)(1352,2146,1405)(1356,1387,1811)(1373,2151,1575)
(1374,1892,1878)(1381,2128,1629)(1389,2008,1496)(1390,1430,1873)
(1393,2106,2054)(1398,1932,1836)(1403,1929,1761)(1404,2131,2086)
(1408,1937,2174)(1410,1562,1489)(1419,1485,2140)(1422,1472,1662)
(1425,1722,1788)(1426,1652,1821)(1441,1827,2003)(1462,1955,1745)
(1466,1972,1963)(1473,1765,1746)(1476,1587,1817)(1479,1686,2006)
(1484,2198,1611)(1525,2014,1574)(1547,2124,1907)(1558,2019,2030)
(1596,1905,1890)(1604,2126,1714)(1621,1678,2095)(1630,2076,1752)
(1651,1768,1881)(1665,2021,1764)(1681,1979,1923)(1727,1911,1789)
(1758,2020,1763)(1783,1988,1947)(1833,2067,2081)(1857,1940,2073)
(1896,2093,2018)(1924,2157,1926)(1938,1999,1995)(1991,2123,2109);