-------
(10, 13122, 7) ALL distance distributions
(7, 13122, 7) has 1 possible DDs: {[6, 84, 504, 1680, 3360, 4032, 2688, 768]}
(8, 13122, 7) has 7 possible DDs: {[0, 48, 168, 1008, 2100, 3696, 3528, 2064, 510], [1, 40, 196, 952, 2170, 3640, 3556, 2056, 511], [2, 32, 224, 896, 2240, 3584, 3584, 2048, 512], [3, 24, 252, 840, 2310, 3528, 3612, 2040, 513], [4, 16, 280, 784, 2380, 3472, 3640, 2032, 514], [5, 8, 308, 728, 2450, 3416, 3668, 2024, 515], [6, 0, 336, 672, 2520, 3360, 3696, 2016, 516]}
(9, 13122, 7) has 100 possible DDs: {[0, 0, 216, 0, 2268, 1512, 4536, 2592, 1674, 324], [0, 1, 208, 28, 2212, 1582, 4480, 2620, 1666, 325], [0, 2, 200, 56, 2156, 1652, 4424, 2648, 1658, 326], [0, 3, 192, 84, 2100, 1722, 4368, 2676, 1650, 327], [0, 4, 184, 112, 2044, 1792, 4312, 2704, 1642, 328], [0, 5, 176, 140, 1988, 1862, 4256, 2732, 1634, 329], [0, 6, 168, 168, 1932, 1932, 4200, 2760, 1626, 330], [0, 7, 160, 196, 1876, 2002, 4144, 2788, 1618, 331], [0, 8, 152, 224, 1820, 2072, 4088, 2816, 1610, 332], [0, 9, 144, 252, 1764, 2142, 4032, 2844, 1602, 333], [0, 10, 136, 280, 1708, 2212, 3976, 2872, 1594, 334], [0, 11, 128, 308, 1652, 2282, 3920, 2900, 1586, 335], [0, 12, 120, 336, 1596, 2352, 3864, 2928, 1578, 336], [0, 13, 112, 364, 1540, 2422, 3808, 2956, 1570, 337], [0, 14, 104, 392, 1484, 2492, 3752, 2984, 1562, 338], [0, 15, 96, 420, 1428, 2562, 3696, 3012, 1554, 339], [0, 16, 88, 448, 1372, 2632, 3640, 3040, 1546, 340], [0, 17, 80, 476, 1316, 2702, 3584, 3068, 1538, 341], [0, 18, 72, 504, 1260, 2772, 3528, 3096, 1530, 342], [0, 19, 64, 532, 1204, 2842, 3472, 3124, 1522, 343], [0, 20, 56, 560, 1148, 2912, 3416, 3152, 1514, 344], [0, 21, 48, 588, 1092, 2982, 3360, 3180, 1506, 345], [0, 22, 40, 616, 1036, 3052, 3304, 3208, 1498, 346], [0, 23, 32, 644, 980, 3122, 3248, 3236, 1490, 347], [0, 24, 24, 672, 924, 3192, 3192, 3264, 1482, 348], [0, 25, 16, 700, 868, 3262, 3136, 3292, 1474, 349], [0, 26, 8, 728, 812, 3332, 3080, 3320, 1466, 350], [0, 27, 0, 756, 756, 3402, 3024, 3348, 1458, 351], [1, 0, 180, 168, 1890, 2016, 4116, 2808, 1611, 332], [1, 1, 172, 196, 1834, 2086, 4060, 2836, 1603, 333], [1, 2, 164, 224, 1778, 2156, 4004, 2864, 1595, 334], [1, 3, 156, 252, 1722, 2226, 3948, 2892, 1587, 335], [1, 4, 148, 280, 1666, 2296, 3892, 2920, 1579, 336], [1, 5, 140, 308, 1610, 2366, 3836, 2948, 1571, 337], [1, 6, 132, 336, 1554, 2436, 3780, 2976, 1563, 338], [1, 7, 124, 364, 1498, 2506, 3724, 3004, 1555, 339], [1, 8, 116, 392, 1442, 2576, 3668, 3032, 1547, 340], [1, 9, 108, 420, 1386, 2646, 3612, 3060, 1539, 341], [1, 10, 100, 448, 1330, 2716, 3556, 3088, 1531, 342], [1, 11, 92, 476, 1274, 2786, 3500, 3116, 1523, 343], [1, 12, 84, 504, 1218, 2856, 3444, 3144, 1515, 344], [1, 13, 76, 532, 1162, 2926, 3388, 3172, 1507, 345], [1, 14, 68, 560, 1106, 2996, 3332, 3200, 1499, 346], [1, 15, 60, 588, 1050, 3066, 3276, 3228, 1491, 347], [1, 16, 52, 616, 994, 3136, 3220, 3256, 1483, 348], [1, 17, 44, 644, 938, 3206, 3164, 3284, 1475, 349], [1, 18, 36, 672, 882, 3276, 3108, 3312, 1467, 350], [1, 19, 28, 700, 826, 3346, 3052, 3340, 1459, 351], [1, 20, 20, 728, 770, 3416, 2996, 3368, 1451, 352], [1, 21, 12, 756, 714, 3486, 2940, 3396, 1443, 353], [1, 22, 4, 784, 658, 3556, 2884, 3424, 1435, 354], [2, 0, 144, 336, 1512, 2520, 3696, 3024, 1548, 340], [2, 1, 136, 364, 1456, 2590, 3640, 3052, 1540, 341], [2, 2, 128, 392, 1400, 2660, 3584, 3080, 1532, 342], [2, 3, 120, 420, 1344, 2730, 3528, 3108, 1524, 343], [2, 4, 112, 448, 1288, 2800, 3472, 3136, 1516, 344], [2, 5, 104, 476, 1232, 2870, 3416, 3164, 1508, 345], [2, 6, 96, 504, 1176, 2940, 3360, 3192, 1500, 346], [2, 7, 88, 532, 1120, 3010, 3304, 3220, 1492, 347], [2, 8, 80, 560, 1064, 3080, 3248, 3248, 1484, 348], [2, 9, 72, 588, 1008, 3150, 3192, 3276, 1476, 349], [2, 10, 64, 616, 952, 3220, 3136, 3304, 1468, 350], [2, 11, 56, 644, 896, 3290, 3080, 3332, 1460, 351], [2, 12, 48, 672, 840, 3360, 3024, 3360, 1452, 352], [2, 13, 40, 700, 784, 3430, 2968, 3388, 1444, 353], [2, 14, 32, 728, 728, 3500, 2912, 3416, 1436, 354], [2, 15, 24, 756, 672, 3570, 2856, 3444, 1428, 355], [2, 16, 16, 784, 616, 3640, 2800, 3472, 1420, 356], [2, 17, 8, 812, 560, 3710, 2744, 3500, 1412, 357], [2, 18, 0, 840, 504, 3780, 2688, 3528, 1404, 358], [3, 0, 108, 504, 1134, 3024, 3276, 3240, 1485, 348], [3, 1, 100, 532, 1078, 3094, 3220, 3268, 1477, 349], [3, 2, 92, 560, 1022, 3164, 3164, 3296, 1469, 350], [3, 3, 84, 588, 966, 3234, 3108, 3324, 1461, 351], [3, 4, 76, 616, 910, 3304, 3052, 3352, 1453, 352], [3, 5, 68, 644, 854, 3374, 2996, 3380, 1445, 353], [3, 6, 60, 672, 798, 3444, 2940, 3408, 1437, 354], [3, 7, 52, 700, 742, 3514, 2884, 3436, 1429, 355], [3, 8, 44, 728, 686, 3584, 2828, 3464, 1421, 356], [3, 9, 36, 756, 630, 3654, 2772, 3492, 1413, 357], [3, 10, 28, 784, 574, 3724, 2716, 3520, 1405, 358], [3, 11, 20, 812, 518, 3794, 2660, 3548, 1397, 359], [3, 12, 12, 840, 462, 3864, 2604, 3576, 1389, 360], [3, 13, 4, 868, 406, 3934, 2548, 3604, 1381, 361], [4, 0, 72, 672, 756, 3528, 2856, 3456, 1422, 356], [4, 1, 64, 700, 700, 3598, 2800, 3484, 1414, 357], [4, 2, 56, 728, 644, 3668, 2744, 3512, 1406, 358], [4, 3, 48, 756, 588, 3738, 2688, 3540, 1398, 359], [4, 4, 40, 784, 532, 3808, 2632, 3568, 1390, 360], [4, 5, 32, 812, 476, 3878, 2576, 3596, 1382, 361], [4, 6, 24, 840, 420, 3948, 2520, 3624, 1374, 362], [4, 7, 16, 868, 364, 4018, 2464, 3652, 1366, 363], [4, 8, 8, 896, 308, 4088, 2408, 3680, 1358, 364], [4, 9, 0, 924, 252, 4158, 2352, 3708, 1350, 365], [5, 0, 36, 840, 378, 4032, 2436, 3672, 1359, 364], [5, 1, 28, 868, 322, 4102, 2380, 3700, 1351, 365], [5, 2, 20, 896, 266, 4172, 2324, 3728, 1343, 366], [5, 3, 12, 924, 210, 4242, 2268, 3756, 1335, 367], [5, 4, 4, 952, 154, 4312, 2212, 3784, 1327, 368], [6, 0, 0, 1008, 0, 4536, 2016, 3888, 1296, 372]}
(10, 13122, 7) has 1446 possible DDs: {[0, 0, 45, 360, 0, 3528, 630, 5400, 1530, 1440, 189], [0, 0, 46, 352, 28, 3472, 700, 5344, 1558, 1432, 190], [0, 0, 47, 344, 56, 3416, 770, 5288, 1586, 1424, 191], [0, 0, 48, 336, 84, 3360, 840, 5232, 1614, 1416, 192], [0, 0, 49, 328, 112, 3304, 910, 5176, 1642, 1408, 193], [0, 0, 50, 320, 140, 3248, 980, 5120, 1670, 1400, 194], [0, 0, 51, 312, 168, 3192, 1050, 5064, 1698, 1392, 195], [0, 0, 52, 304, 196, 3136, 1120, 5008, 1726, 1384, 196], [0, 0, 53, 296, 224, 3080, 1190, 4952, 1754, 1376, 197], [0, 0, 54, 288, 252, 3024, 1260, 4896, 1782, 1368, 198], [0, 0, 55, 280, 280, 2968, 1330, 4840, 1810, 1360, 199], [0, 0, 56, 272, 308, 2912, 1400, 4784, 1838, 1352, 200], [0, 0, 57, 264, 336, 2856, 1470, 4728, 1866, 1344, 201], [0, 0, 58, 256, 364, 2800, 1540, 4672, 1894, 1336, 202], [0, 0, 59, 248, 392, 2744, 1610, 4616, 1922, 1328, 203], [0, 0, 60, 240, 420, 2688, 1680, 4560, 1950, 1320, 204], [0, 0, 61, 232, 448, 2632, 1750, 4504, 1978, 1312, 205], [0, 0, 62, 224, 476, 2576, 1820, 4448, 2006, 1304, 206], [0, 0, 63, 216, 504, 2520, 1890, 4392, 2034, 1296, 207], [0, 0, 64, 208, 532, 2464, 1960, 4336, 2062, 1288, 208], [0, 0, 65, 200, 560, 2408, 2030, 4280, 2090, 1280, 209], [0, 0, 66, 192, 588, 2352, 2100, 4224, 2118, 1272, 210], [0, 0, 67, 184, 616, 2296, 2170, 4168, 2146, 1264, 211], [0, 0, 68, 176, 644, 2240, 2240, 4112, 2174, 1256, 212], [0, 0, 69, 168, 672, 2184, 2310, 4056, 2202, 1248, 213], [0, 0, 70, 160, 700, 2128, 2380, 4000, 2230, 1240, 214], [0, 0, 71, 152, 728, 2072, 2450, 3944, 2258, 1232, 215], [0, 0, 72, 144, 756, 2016, 2520, 3888, 2286, 1224, 216], [0, 0, 73, 136, 784, 1960, 2590, 3832, 2314, 1216, 217], [0, 0, 74, 128, 812, 1904, 2660, 3776, 2342, 1208, 218], [0, 0, 75, 120, 840, 1848, 2730, 3720, 2370, 1200, 219], [0, 0, 76, 112, 868, 1792, 2800, 3664, 2398, 1192, 220], [0, 0, 77, 104, 896, 1736, 2870, 3608, 2426, 1184, 221], [0, 0, 78, 96, 924, 1680, 2940, 3552, 2454, 1176, 222], [0, 0, 79, 88, 952, 1624, 3010, 3496, 2482, 1168, 223], [0, 0, 80, 80, 980, 1568, 3080, 3440, 2510, 1160, 224], [0, 0, 81, 72, 1008, 1512, 3150, 3384, 2538, 1152, 225], [0, 0, 82, 64, 1036, 1456, 3220, 3328, 2566, 1144, 226], [0, 0, 83, 56, 1064, 1400, 3290, 3272, 2594, 1136, 227], [0, 0, 84, 48, 1092, 1344, 3360, 3216, 2622, 1128, 228], [0, 0, 85, 40, 1120, 1288, 3430, 3160, 2650, 1120, 229], [0, 0, 86, 32, 1148, 1232, 3500, 3104, 2678, 1112, 230], [0, 0, 87, 24, 1176, 1176, 3570, 3048, 2706, 1104, 231], [0, 0, 88, 16, 1204, 1120, 3640, 2992, 2734, 1096, 232], [0, 0, 89, 8, 1232, 1064, 3710, 2936, 2762, 1088, 233], [0, 0, 90, 0, 1260, 1008, 3780, 2880, 2790, 1080, 234], [0, 1, 39, 372, 0, 3486, 714, 5316, 1578, 1425, 191], [0, 1, 40, 364, 28, 3430, 784, 5260, 1606, 1417, 192], [0, 1, 41, 356, 56, 3374, 854, 5204, 1634, 1409, 193], [0, 1, 42, 348, 84, 3318, 924, 5148, 1662, 1401, 194], [0, 1, 43, 340, 112, 3262, 994, 5092, 1690, 1393, 195], [0, 1, 44, 332, 140, 3206, 1064, 5036, 1718, 1385, 196], [0, 1, 45, 324, 168, 3150, 1134, 4980, 1746, 1377, 197], [0, 1, 46, 316, 196, 3094, 1204, 4924, 1774, 1369, 198], [0, 1, 47, 308, 224, 3038, 1274, 4868, 1802, 1361, 199], [0, 1, 48, 300, 252, 2982, 1344, 4812, 1830, 1353, 200], [0, 1, 49, 292, 280, 2926, 1414, 4756, 1858, 1345, 201], [0, 1, 50, 284, 308, 2870, 1484, 4700, 1886, 1337, 202], [0, 1, 51, 276, 336, 2814, 1554, 4644, 1914, 1329, 203], [0, 1, 52, 268, 364, 2758, 1624, 4588, 1942, 1321, 204], [0, 1, 53, 260, 392, 2702, 1694, 4532, 1970, 1313, 205], [0, 1, 54, 252, 420, 2646, 1764, 4476, 1998, 1305, 206], [0, 1, 55, 244, 448, 2590, 1834, 4420, 2026, 1297, 207], [0, 1, 56, 236, 476, 2534, 1904, 4364, 2054, 1289, 208], [0, 1, 57, 228, 504, 2478, 1974, 4308, 2082, 1281, 209], [0, 1, 58, 220, 532, 2422, 2044, 4252, 2110, 1273, 210], [0, 1, 59, 212, 560, 2366, 2114, 4196, 2138, 1265, 211], [0, 1, 60, 204, 588, 2310, 2184, 4140, 2166, 1257, 212], [0, 1, 61, 196, 616, 2254, 2254, 4084, 2194, 1249, 213], [0, 1, 62, 188, 644, 2198, 2324, 4028, 2222, 1241, 214], [0, 1, 63, 180, 672, 2142, 2394, 3972, 2250, 1233, 215], [0, 1, 64, 172, 700, 2086, 2464, 3916, 2278, 1225, 216], [0, 1, 65, 164, 728, 2030, 2534, 3860, 2306, 1217, 217], [0, 1, 66, 156, 756, 1974, 2604, 3804, 2334, 1209, 218], [0, 1, 67, 148, 784, 1918, 2674, 3748, 2362, 1201, 219], [0, 1, 68, 140, 812, 1862, 2744, 3692, 2390, 1193, 220], [0, 1, 69, 132, 840, 1806, 2814, 3636, 2418, 1185, 221], [0, 1, 70, 124, 868, 1750, 2884, 3580, 2446, 1177, 222], [0, 1, 71, 116, 896, 1694, 2954, 3524, 2474, 1169, 223], [0, 1, 72, 108, 924, 1638, 3024, 3468, 2502, 1161, 224], [0, 1, 73, 100, 952, 1582, 3094, 3412, 2530, 1153, 225], [0, 1, 74, 92, 980, 1526, 3164, 3356, 2558, 1145, 226], [0, 1, 75, 84, 1008, 1470, 3234, 3300, 2586, 1137, 227], [0, 1, 76, 76, 1036, 1414, 3304, 3244, 2614, 1129, 228], [0, 1, 77, 68, 1064, 1358, 3374, 3188, 2642, 1121, 229], [0, 1, 78, 60, 1092, 1302, 3444, 3132, 2670, 1113, 230], [0, 1, 79, 52, 1120, 1246, 3514, 3076, 2698, 1105, 231], [0, 1, 80, 44, 1148, 1190, 3584, 3020, 2726, 1097, 232], [0, 1, 81, 36, 1176, 1134, 3654, 2964, 2754, 1089, 233], [0, 1, 82, 28, 1204, 1078, 3724, 2908, 2782, 1081, 234], [0, 1, 83, 20, 1232, 1022, 3794, 2852, 2810, 1073, 235], [0, 1, 84, 12, 1260, 966, 3864, 2796, 2838, 1065, 236], [0, 1, 85, 4, 1288, 910, 3934, 2740, 2866, 1057, 237], [0, 2, 33, 384, 0, 3444, 798, 5232, 1626, 1410, 193], [0, 2, 34, 376, 28, 3388, 868, 5176, 1654, 1402, 194], [0, 2, 35, 368, 56, 3332, 938, 5120, 1682, 1394, 195], [0, 2, 36, 360, 84, 3276, 1008, 5064, 1710, 1386, 196], [0, 2, 37, 352, 112, 3220, 1078, 5008, 1738, 1378, 197], [0, 2, 38, 344, 140, 3164, 1148, 4952, 1766, 1370, 198], [0, 2, 39, 336, 168, 3108, 1218, 4896, 1794, 1362, 199], [0, 2, 40, 328, 196, 3052, 1288, 4840, 1822, 1354, 200], [0, 2, 41, 320, 224, 2996, 1358, 4784, 1850, 1346, 201], [0, 2, 42, 312, 252, 2940, 1428, 4728, 1878, 1338, 202], [0, 2, 43, 304, 280, 2884, 1498, 4672, 1906, 1330, 203], [0, 2, 44, 296, 308, 2828, 1568, 4616, 1934, 1322, 204], [0, 2, 45, 288, 336, 2772, 1638, 4560, 1962, 1314, 205], [0, 2, 46, 280, 364, 2716, 1708, 4504, 1990, 1306, 206], [0, 2, 47, 272, 392, 2660, 1778, 4448, 2018, 1298, 207], [0, 2, 48, 264, 420, 2604, 1848, 4392, 2046, 1290, 208], [0, 2, 49, 256, 448, 2548, 1918, 4336, 2074, 1282, 209], [0, 2, 50, 248, 476, 2492, 1988, 4280, 2102, 1274, 210], [0, 2, 51, 240, 504, 2436, 2058, 4224, 2130, 1266, 211], [0, 2, 52, 232, 532, 2380, 2128, 4168, 2158, 1258, 212], [0, 2, 53, 224, 560, 2324, 2198, 4112, 2186, 1250, 213], [0, 2, 54, 216, 588, 2268, 2268, 4056, 2214, 1242, 214], [0, 2, 55, 208, 616, 2212, 2338, 4000, 2242, 1234, 215], [0, 2, 56, 200, 644, 2156, 2408, 3944, 2270, 1226, 216], [0, 2, 57, 192, 672, 2100, 2478, 3888, 2298, 1218, 217], [0, 2, 58, 184, 700, 2044, 2548, 3832, 2326, 1210, 218], [0, 2, 59, 176, 728, 1988, 2618, 3776, 2354, 1202, 219], [0, 2, 60, 168, 756, 1932, 2688, 3720, 2382, 1194, 220], [0, 2, 61, 160, 784, 1876, 2758, 3664, 2410, 1186, 221], [0, 2, 62, 152, 812, 1820, 2828, 3608, 2438, 1178, 222], [0, 2, 63, 144, 840, 1764, 2898, 3552, 2466, 1170, 223], [0, 2, 64, 136, 868, 1708, 2968, 3496, 2494, 1162, 224], [0, 2, 65, 128, 896, 1652, 3038, 3440, 2522, 1154, 225], [0, 2, 66, 120, 924, 1596, 3108, 3384, 2550, 1146, 226], [0, 2, 67, 112, 952, 1540, 3178, 3328, 2578, 1138, 227], [0, 2, 68, 104, 980, 1484, 3248, 3272, 2606, 1130, 228], [0, 2, 69, 96, 1008, 1428, 3318, 3216, 2634, 1122, 229], [0, 2, 70, 88, 1036, 1372, 3388, 3160, 2662, 1114, 230], [0, 2, 71, 80, 1064, 1316, 3458, 3104, 2690, 1106, 231], [0, 2, 72, 72, 1092, 1260, 3528, 3048, 2718, 1098, 232], [0, 2, 73, 64, 1120, 1204, 3598, 2992, 2746, 1090, 233], [0, 2, 74, 56, 1148, 1148, 3668, 2936, 2774, 1082, 234], [0, 2, 75, 48, 1176, 1092, 3738, 2880, 2802, 1074, 235], [0, 2, 76, 40, 1204, 1036, 3808, 2824, 2830, 1066, 236], [0, 2, 77, 32, 1232, 980, 3878, 2768, 2858, 1058, 237], [0, 2, 78, 24, 1260, 924, 3948, 2712, 2886, 1050, 238], [0, 2, 79, 16, 1288, 868, 4018, 2656, 2914, 1042, 239], [0, 2, 80, 8, 1316, 812, 4088, 2600, 2942, 1034, 240], [0, 2, 81, 0, 1344, 756, 4158, 2544, 2970, 1026, 241], [0, 3, 27, 396, 0, 3402, 882, 5148, 1674, 1395, 195], [0, 3, 28, 388, 28, 3346, 952, 5092, 1702, 1387, 196], [0, 3, 29, 380, 56, 3290, 1022, 5036, 1730, 1379, 197], [0, 3, 30, 372, 84, 3234, 1092, 4980, 1758, 1371, 198], [0, 3, 31, 364, 112, 3178, 1162, 4924, 1786, 1363, 199], [0, 3, 32, 356, 140, 3122, 1232, 4868, 1814, 1355, 200], [0, 3, 33, 348, 168, 3066, 1302, 4812, 1842, 1347, 201], [0, 3, 34, 340, 196, 3010, 1372, 4756, 1870, 1339, 202], [0, 3, 35, 332, 224, 2954, 1442, 4700, 1898, 1331, 203], [0, 3, 36, 324, 252, 2898, 1512, 4644, 1926, 1323, 204], [0, 3, 37, 316, 280, 2842, 1582, 4588, 1954, 1315, 205], [0, 3, 38, 308, 308, 2786, 1652, 4532, 1982, 1307, 206], [0, 3, 39, 300, 336, 2730, 1722, 4476, 2010, 1299, 207], [0, 3, 40, 292, 364, 2674, 1792, 4420, 2038, 1291, 208], [0, 3, 41, 284, 392, 2618, 1862, 4364, 2066, 1283, 209], [0, 3, 42, 276, 420, 2562, 1932, 4308, 2094, 1275, 210], 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