Encapsulation -- ML-KEM-1024
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m: 034FF14A56249C2521D4279EBA3D04931CC892BBC45002B5B33D9F0188ACBAF6

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r: 8A6BF0ABC0660F5EAF82FC503DA73AA76A2BD0D8E85424D27F4F750AC3CCE15E
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NTTInverse(BHat * rHat): [[2728, 2304, 2829, 2833, 2625, 1826, 1467, 2857, 59, 3288, 577, 376, 3174, 1542, 1012, 1689, 926, 1310, 311, 1655, 2244, 3216, 837, 3012, 3150, 2318, 2182, 2567, 824, 1286, 891, 674, 1539, 3002, 175, 3299, 815, 1447, 284, 3224, 353, 257, 1842, 811, 288, 496, 551, 3101, 3221, 1527, 1446, 2279, 498, 1731, 1763, 1165, 568, 953, 2071, 1559, 2967, 1778, 353, 1027, 2928, 3209, 998, 1065, 3066, 2081, 3137, 897, 1825, 2258, 401, 2417, 2783, 1297, 431, 2029, 1012, 1197, 1993, 1339, 1674, 950, 2893, 3028, 3269, 2453, 2228, 2556, 418, 1874, 792, 254, 253, 436, 473, 1571, 1459, 980, 2296, 2527, 547, 2299, 3215, 3220, 3292, 2644, 2939, 3073, 500, 3084, 2883, 138, 1781, 3120, 3129, 1320, 95, 201, 1850, 2622, 2788, 364, 2424, 508, 2011, 689, 2130, 2770, 1817, 938, 3130, 853, 878, 188, 2862, 91, 3055, 2944, 646, 3070, 3264, 145, 1708, 1713, 520, 2190, 283, 472, 1842, 1878, 3277, 1862, 1835, 3317, 818, 1899, 2287, 1418, 2458, 3167, 1572, 3114, 1667, 899, 2027, 528, 2017, 199, 1982, 485, 1139, 3241, 2560, 918, 665, 2345, 1483, 2717, 2134, 3193, 1540, 977, 1919, 2029, 2493, 2140, 242, 2093, 280, 2944, 533, 2427, 2647, 3151, 3039, 1297, 2561, 1283, 2802, 1925, 2968, 1887, 335, 763, 1091, 1953, 665, 1046, 2485, 2470, 1043, 866, 1944, 1177, 1944, 1702, 2378, 3114, 1789, 2269, 810, 1162, 700, 3234, 635, 2606, 438, 2619, 3169, 1240, 1872, 1098, 2608, 654, 1668, 393, 1334, 3322, 2884, 2581, 1959, 2831, 1913, 1758, 1996, 1996, 3163, 3095, 1053, 1390, 1464, 1648],
[1569, 2344, 876, 650, 2412, 697, 3077, 236, 1862, 1645, 955, 3257, 920, 1123, 2068, 2601, 463, 1294, 1418, 527, 1123, 88, 106, 839, 2029, 3247, 374, 1607, 2576, 2305, 2402, 333, 2861, 125, 710, 3202, 545, 2265, 1184, 2044, 1172, 2624, 2725, 1821, 3210, 1643, 1265, 1081, 1029, 2086, 1619, 803, 22, 2330, 1617, 220, 2560, 1399, 1994, 2741, 2972, 2750, 2863, 2690, 2273, 1715, 2811, 1293, 2335, 3089, 2287, 2508, 3054, 1353, 1539, 3071, 2950, 56, 3147, 1778, 2417, 340, 404, 2208, 2937, 420, 1936, 2998, 481, 3321, 194, 1111, 71, 999, 450, 496, 3157, 1670, 329, 2883, 594, 1938, 2728, 1713, 2188, 2330, 1174, 427, 1051, 289, 2200, 1509, 1185, 1691, 1206, 2931, 1463, 2824, 1545, 3005, 3123, 1975, 1099, 1683, 1448, 3155, 2111, 2524, 2827, 1125, 179, 1429, 1625, 73, 1843, 2674, 2811, 724, 2916, 1958, 1462, 1449, 2466, 1743, 1130, 1663, 494, 2207, 2234, 2156, 1853, 2817, 570, 3004, 2976, 1272, 670, 2828, 2385, 124, 1714, 486, 2372, 955, 1265, 879, 3079, 2080, 1854, 579, 3218, 1740, 1938, 820, 2064, 1998, 3017, 2329, 797, 1154, 659, 821, 2385, 2181, 3149, 2134, 2848, 1691, 36, 490, 1024, 345, 3211, 1268, 1796, 1216, 17, 2878, 1658, 94, 1077, 3145, 2226, 2840, 945, 1876, 2850, 2053, 2261, 2871, 1835, 171, 2216, 3160, 83, 2986, 1016, 2546, 2772, 1613, 2387, 3108, 2953, 1225, 1296, 858, 2014, 1446, 3243, 2490, 521, 2225, 2228, 1960, 2402, 2603, 2304, 1005, 1025, 1579, 3107, 1329, 1374, 1722, 2064, 3035, 290, 2169, 2141, 2715, 2493, 3259, 610, 1423, 846, 1488],
[2425, 529, 3010, 2623, 707, 1719, 1392, 697, 69, 1760, 2602, 841, 2529, 245, 3266, 1397, 406, 2831, 2126, 1601, 1242, 2769, 2400, 1585, 2104, 495, 444, 235, 2172, 1364, 2942, 3237, 1084, 1839, 2895, 1196, 2250, 1591, 573, 2794, 1307, 3, 1620, 2694, 2657, 2972, 1558, 2406, 1405, 2983, 2700, 1915, 2909, 852, 501, 3004, 2775, 1964, 1464, 1304, 2225, 992, 2283, 491, 414, 3224, 2212, 2651, 1239, 1968, 1412, 914, 3300, 2713, 1696, 906, 2662, 2527, 2346, 2321, 3141, 2169, 1518, 1788, 351, 122, 193, 2146, 2173, 1351, 2225, 2633, 1274, 3062, 2549, 2428, 3159, 2925, 2320, 2078, 2999, 2581, 2851, 840, 900, 1349, 92, 440, 2232, 2015, 1139, 2161, 2831, 2480, 2433, 2833, 316, 1182, 3037, 1588, 3197, 758, 687, 596, 1977, 219, 2611, 905, 1864, 234, 44, 2359, 3216, 313, 3142, 829, 662, 728, 12, 1995, 2044, 2098, 3158, 2037, 1008, 3174, 56, 3185, 10, 1905, 1383, 584, 2759, 489, 2213, 2450, 230, 54, 1295, 2158, 3095, 2907, 1937, 2320, 0, 3227, 2886, 1971, 2864, 2748, 1375, 2674, 2281, 1503, 2115, 1325, 288, 795, 3273, 505, 1494, 2495, 368, 3014, 3070, 1503, 1779, 47, 441, 2063, 1099, 2963, 1246, 1129, 1165, 2571, 761, 2194, 906, 1596, 229, 890, 92, 1479, 2960, 665, 1742, 2903, 816, 1997, 22, 1835, 2640, 1128, 2758, 2264, 1035, 1646, 277, 2288, 90, 2978, 922, 2276, 3048, 1626, 2210, 1592, 2268, 2268, 180, 2605, 2660, 786, 37, 2195, 45, 2075, 2490, 2485, 1153, 132, 2656, 619, 883, 237, 1363, 239, 773, 2909, 2026, 829, 606, 2009, 2039, 394],
[820, 1829, 641, 967, 2242, 772, 435, 1740, 1911, 1805, 581, 2080, 3116, 22, 2646, 3253, 543, 1048, 1517, 2828, 948, 2801, 1211, 3222, 1466, 2299, 583, 785, 3287, 234, 2877, 1666, 1705, 1421, 414, 1021, 1814, 3027, 452, 323, 2367, 3296, 265, 466, 1450, 895, 1924, 2906, 3168, 92, 6, 3022, 1080, 57, 3115, 1047, 95, 2807, 2773, 1388, 1697, 178, 2042, 2612, 980, 2645, 2253, 1960, 654, 1216, 706, 2110, 1440, 1001, 2487, 251, 2494, 1278, 487, 1936, 1539, 436, 1580, 2042, 2811, 1530, 1239, 2147, 720, 6, 2698, 1710, 1759, 1747, 896, 2876, 1075, 511, 2132, 784, 1956, 2623, 3038, 836, 977, 3066, 1781, 332, 1054, 1937, 2436, 372, 1052, 2296, 2089, 2565, 996, 2935, 3196, 3080, 2166, 2104, 2135, 3025, 438, 2998, 2138, 2857, 2635, 2116, 2009, 1602, 180, 866, 1630, 2814, 722, 3053, 2808, 1552, 1657, 3196, 2219, 3253, 2591, 998, 3144, 985, 1499, 1438, 1052, 1517, 2243, 1454, 1895, 966, 2020, 1742, 2090, 2468, 401, 1129, 2235, 1099, 2836, 1429, 1401, 2931, 2868, 474, 831, 532, 199, 3113, 1515, 3105, 3301, 674, 1224, 977, 2388, 265, 1627, 3146, 3318, 3303, 330, 1566, 1180, 371, 149, 1469, 1678, 1804, 3213, 1902, 1584, 1369, 749, 2116, 1424, 897, 1940, 3255, 1337, 944, 2899, 2317, 471, 777, 808, 2697, 2302, 2191, 2402, 2506, 1003, 2978, 2448, 2896, 2783, 2550, 1963, 857, 2567, 1079, 392, 21, 2708, 3274, 2598, 1661, 2575, 1637, 587, 394, 2874, 2117, 2723, 3065, 565, 40, 1101, 64, 2879, 2464, 2470, 947, 2685, 1563, 1115, 399, 2129, 951, 558, 400]]
u = NTTInverse(BHat * rHat) + e1: [[2726, 2304, 2828, 2833, 2625, 1826, 1467, 2859, 57, 3288, 576, 375, 3174, 1542, 1012, 1687, 927, 1310, 312, 1655, 2246, 3215, 838, 3012, 3149, 2319, 2181, 2568, 825, 1285, 891, 673, 1540, 3000, 174, 3299, 816, 1448, 285, 3224, 355, 256, 1844, 810, 289, 495, 553, 3103, 3221, 1528, 1445, 2279, 497, 1731, 1764, 1164, 568, 953, 2070, 1560, 2966, 1777, 353, 1027, 2928, 3208, 997, 1065, 3066, 2081, 3138, 895, 1826, 2259, 401, 2417, 2784, 1298, 430, 2029, 1011, 1195, 1993, 1341, 1675, 951, 2892, 3029, 3270, 2452, 2229, 2556, 419, 1875, 792, 254, 253, 436, 471, 1572, 1458, 980, 2297, 2526, 547, 2299, 3215, 3221, 3293, 2645, 2939, 3073, 501, 3082, 2884, 138, 1781, 3119, 3129, 1319, 94, 202, 1849, 2622, 2789, 365, 2425, 510, 2012, 688, 2128, 2769, 1817, 938, 3131, 853, 878, 187, 2863, 91, 3054, 2943, 648, 3069, 3264, 146, 1706, 1714, 519, 2189, 282, 474, 1841, 1877, 3279, 1862, 1836, 3317, 818, 1899, 2287, 1419, 2459, 3167, 1572, 3112, 1666, 901, 2027, 528, 2017, 199, 1981, 484, 1140, 3241, 2560, 918, 667, 2343, 1483, 2718, 2135, 3192, 1540, 975, 1920, 2030, 2491, 2141, 242, 2094, 280, 2944, 532, 2427, 2648, 3150, 3041, 1297, 2560, 1282, 2801, 1925, 2968, 1886, 333, 763, 1093, 1953, 667, 1047, 2483, 2470, 1043, 866, 1944, 1177, 1945, 1701, 2378, 3112, 1787, 2269, 809, 1161, 698, 3234, 634, 2606, 438, 2620, 3168, 1239, 1871, 1099, 2609, 653, 1668, 394, 1334, 3322, 2883, 2580, 1959, 2830, 1912, 1758, 1995, 1996, 3162, 3096, 1053, 1390, 1463, 1648],
[1570, 2343, 876, 650, 2411, 697, 3077, 236, 1861, 1645, 956, 3257, 921, 1124, 2069, 2601, 463, 1295, 1417, 527, 1123, 88, 108, 838, 2029, 3248, 374, 1609, 2576, 2306, 2402, 334, 2859, 125, 711, 3203, 545, 2264, 1185, 2043, 1173, 2622, 2725, 1822, 3208, 1642, 1264, 1082, 1031, 2087, 1620, 804, 21, 2329, 1615, 221, 2560, 1399, 1992, 2739, 2972, 2749, 2863, 2690, 2272, 1714, 2810, 1293, 2334, 3089, 2286, 2509, 3053, 1352, 1541, 3071, 2949, 57, 3147, 1779, 2418, 340, 405, 2210, 2936, 418, 1938, 2999, 480, 3321, 194, 1111, 71, 998, 450, 495, 3158, 1671, 329, 2882, 592, 1938, 2727, 1714, 2188, 2329, 1172, 428, 1051, 289, 2202, 1510, 1185, 1691, 1207, 2929, 1464, 2826, 1544, 3006, 3122, 1976, 1099, 1683, 1448, 3154, 2111, 2522, 2827, 1124, 178, 1428, 1624, 73, 1843, 2674, 2812, 723, 2918, 1957, 1463, 1451, 2465, 1742, 1131, 1662, 495, 2206, 2235, 2156, 1852, 2817, 570, 3005, 2975, 1271, 669, 2829, 2386, 124, 1713, 485, 2371, 954, 1265, 878, 3078, 2079, 1854, 581, 3218, 1740, 1937, 818, 2066, 1998, 3016, 2330, 795, 1154, 658, 820, 2385, 2180, 3149, 2136, 2847, 1691, 35, 491, 1024, 346, 3211, 1267, 1795, 1218, 19, 2878, 1656, 95, 1079, 3145, 2227, 2840, 945, 1877, 2852, 2052, 2261, 2872, 1835, 171, 2217, 3158, 83, 2987, 1016, 2547, 2772, 1613, 2386, 3107, 2951, 1225, 1295, 860, 2015, 1447, 3242, 2489, 522, 2225, 2228, 1962, 2402, 2603, 2304, 1005, 1025, 1579, 3107, 1328, 1374, 1723, 2064, 3037, 291, 2168, 2140, 2715, 2493, 3260, 610, 1423, 846, 1489],
[2427, 528, 3009, 2623, 707, 1720, 1391, 696, 68, 1760, 2601, 843, 2530, 246, 3266, 1397, 407, 2831, 2125, 1602, 1242, 2769, 2400, 1586, 2106, 497, 443, 236, 2173, 1365, 2942, 3237, 1083, 1840, 2895, 1195, 2250, 1590, 572, 2795, 1308, 3, 1621, 2695, 2657, 2971, 1560, 2406, 1405, 2983, 2701, 1914, 2909, 851, 501, 3002, 2775, 1962, 1464, 1305, 2226, 990, 2282, 489, 415, 3224, 2213, 2652, 1239, 1970, 1413, 914, 3299, 2714, 1696, 905, 2661, 2527, 2346, 2319, 3143, 2167, 1517, 1788, 351, 122, 195, 2147, 2172, 1350, 2224, 2632, 1273, 3062, 2549, 2430, 3161, 2926, 2319, 2078, 2999, 2582, 2852, 840, 900, 1349, 94, 441, 2232, 2014, 1139, 2161, 2832, 2479, 2434, 2832, 316, 1183, 3037, 1588, 3198, 757, 685, 595, 1977, 220, 2610, 905, 1865, 235, 44, 2359, 3215, 315, 3142, 829, 663, 728, 12, 1994, 2044, 2099, 3159, 2037, 1007, 3173, 57, 3186, 10, 1905, 1383, 583, 2759, 488, 2215, 2450, 229, 53, 1294, 2158, 3096, 2908, 1937, 2322, 0, 3228, 2885, 1971, 2865, 2750, 1374, 2675, 2282, 1502, 2116, 1325, 287, 795, 3273, 506, 1493, 2496, 368, 3015, 3070, 1504, 1778, 48, 440, 2064, 1098, 2963, 1245, 1130, 1166, 2573, 760, 2194, 905, 1597, 230, 891, 91, 1479, 2960, 663, 1741, 2902, 818, 1996, 24, 1836, 2640, 1130, 2758, 2264, 1035, 1646, 278, 2288, 90, 2977, 922, 2275, 3048, 1627, 2208, 1592, 2268, 2269, 181, 2603, 2660, 786, 38, 2196, 45, 2075, 2491, 2485, 1152, 132, 2657, 619, 883, 236, 1364, 238, 773, 2910, 2026, 829, 608, 2007, 2041, 393],
[821, 1830, 641, 966, 2243, 774, 434, 1738, 1911, 1805, 581, 2078, 3115, 22, 2645, 3254, 543, 1048, 1517, 2827, 947, 2801, 1211, 3222, 1466, 2299, 583, 784, 3287, 236, 2877, 1666, 1706, 1420, 414, 1022, 1813, 3027, 451, 324, 2366, 3297, 266, 468, 1449, 896, 1924, 2908, 3170, 92, 4, 3020, 1079, 59, 3116, 1048, 95, 2806, 2772, 1389, 1696, 177, 2044, 2613, 980, 2647, 2255, 1960, 654, 1216, 707, 2111, 1440, 1001, 2486, 251, 2494, 1279, 487, 1936, 1540, 437, 1580, 2041, 2811, 1531, 1239, 2146, 720, 7, 2699, 1709, 1758, 1746, 895, 2874, 1075, 509, 2134, 784, 1955, 2622, 3039, 835, 978, 3066, 1780, 331, 1054, 1936, 2436, 372, 1053, 2296, 2089, 2564, 995, 2935, 3197, 3082, 2165, 2103, 2137, 3025, 437, 2999, 2139, 2857, 2635, 2117, 2008, 1602, 178, 867, 1629, 2815, 721, 3053, 2809, 1553, 1657, 3197, 2220, 3253, 2590, 999, 3143, 986, 1500, 1438, 1051, 1516, 2244, 1455, 1894, 966, 2020, 1741, 2089, 2467, 401, 1130, 2235, 1101, 2837, 1430, 1403, 2932, 2869, 474, 831, 532, 200, 3112, 1516, 3106, 3302, 676, 1224, 977, 2386, 265, 1627, 3146, 3319, 3301, 330, 1568, 1178, 370, 150, 1469, 1677, 1803, 3211, 1902, 1586, 1369, 749, 2116, 1425, 896, 1941, 3254, 1338, 945, 2901, 2316, 471, 776, 808, 2697, 2301, 2192, 2402, 2506, 1004, 2979, 2449, 2896, 2784, 2550, 1963, 857, 2565, 1079, 391, 20, 2708, 3273, 2597, 1661, 2576, 1636, 587, 395, 2874, 2118, 2723, 3063, 564, 41, 1100, 64, 2880, 2463, 2469, 947, 2685, 1563, 1115, 400, 2131, 953, 560, 400]]

mu: [1665, 1665, 0, 0, 0, 0, 0, 0, 1665, 1665, 1665, 1665, 0, 0, 1665, 0, 1665, 0, 0, 0, 1665, 1665, 1665, 1665, 0, 1665, 0, 1665, 0, 0, 1665, 0, 0, 1665, 1665, 0, 1665, 0, 1665, 0, 0, 0, 1665, 0, 0, 1665, 0, 0, 0, 0, 1665, 1665, 1665, 0, 0, 1665, 1665, 0, 1665, 0, 0, 1665, 0, 0, 1665, 0, 0, 0, 0, 1665, 0, 0, 0, 0, 1665, 0, 1665, 0, 1665, 1665, 1665, 1665, 1665, 0, 0, 1665, 0, 0, 0, 1665, 1665, 1665, 1665, 0, 0, 1665, 0, 1665, 0, 1665, 1665, 1665, 0, 1665, 1665, 0, 1665, 1665, 1665, 1665, 0, 0, 0, 0, 1665, 0, 0, 0, 0, 0, 1665, 1665, 0, 0, 1665, 0, 0, 1665, 0, 0, 1665, 1665, 1665, 0, 0, 0, 0, 0, 0, 1665, 0, 0, 1665, 1665, 0, 1665, 0, 0, 1665, 0, 0, 1665, 1665, 1665, 0, 1665, 1665, 1665, 0, 1665, 0, 0, 1665, 0, 0, 0, 1665, 1665, 0, 0, 0, 0, 1665, 0, 1665, 0, 0, 1665, 0, 0, 0, 0, 0, 0, 1665, 0, 1665, 0, 1665, 1665, 0, 1665, 1665, 1665, 0, 0, 1665, 1665, 0, 1665, 1665, 0, 1665, 1665, 1665, 1665, 0, 0, 1665, 1665, 1665, 1665, 1665, 0, 0, 1665, 1665, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1665, 0, 0, 0, 1665, 0, 0, 1665, 1665, 0, 1665, 0, 1665, 0, 1665, 0, 1665, 1665, 1665, 0, 1665, 0, 1665, 1665, 0, 1665, 1665, 1665, 1665]
tHat^T * rHat: [2832, 998, 1041, 112, 1377, 3292, 2245, 2778, 1275, 131, 1065, 1532, 1554, 3218, 321, 64, 713, 2494, 1080, 1187, 1448, 2307, 2085, 600, 1497, 1186, 243, 356, 97, 3068, 2998, 1766, 1245, 1393, 1446, 70, 3167, 1797, 393, 2580, 789, 593, 2041, 422, 1847, 1834, 2425, 3181, 54, 1941, 2527, 1251, 828, 1724, 586, 789, 1630, 721, 2239, 1085, 259, 2515, 217, 3208, 930, 2981, 3085, 3225, 851, 2573, 2518, 609, 2072, 3236, 2034, 2805, 1671, 2242, 3032, 2593, 1943, 176, 895, 196, 885, 920, 3047, 2375, 646, 3039, 2687, 1152, 785, 1572, 207, 2196, 2962, 866, 523, 1363, 2262, 2797, 1400, 1828, 2406, 1579, 680, 1879, 180, 1614, 116, 3168, 2110, 3106, 2738, 3256, 3185, 2813, 2433, 2343, 64, 841, 2623, 3211, 2036, 123, 2832, 2922, 1144, 2110, 2682, 1124, 862, 1205, 524, 3286, 439, 3121, 2484, 1957, 1531, 1002, 2941, 3205, 982, 1679, 1973, 1222, 1430, 1574, 2859, 10, 345, 344, 1108, 1822, 784, 2299, 2135, 2346, 3206, 2656, 2077, 757, 1195, 303, 1971, 706, 993, 1931, 2663, 1192, 3152, 2734, 707, 3013, 242, 2335, 2685, 1550, 1923, 1604, 2041, 2685, 2607, 1429, 2139, 2041, 2099, 1781, 1376, 1258, 2320, 346, 1478, 3321, 572, 1093, 316, 787, 2434, 1114, 1757, 1293, 3051, 1743, 1842, 1527, 2670, 822, 2980, 1818, 2503, 1163, 214, 3061, 1190, 2501, 1650, 180, 64, 2031, 2924, 1525, 3214, 2702, 715, 3050, 1714, 3228, 1269, 155, 11, 1043, 2307, 3294, 3308, 2766, 67, 563, 765, 2037, 125, 1582, 810, 2910, 1856, 2345, 3146, 3039, 3002, 1274, 2109, 2488, 2045, 520]
NTTInverse(tHat^T * rHat): [2232, 1324, 153, 262, 1847, 1416, 1179, 704, 88, 3232, 1082, 2292, 1628, 1916, 3032, 2802, 1858, 890, 2481, 1541, 804, 1566, 2553, 2200, 2924, 2688, 0, 2050, 2407, 3241, 2099, 1311, 2358, 528, 1275, 386, 552, 2798, 924, 2192, 1443, 1889, 2438, 2186, 3233, 2258, 1093, 726, 2741, 2431, 651, 870, 1376, 2355, 168, 2366, 692, 2672, 1340, 1489, 1460, 2443, 284, 256, 975, 2416, 2213, 831, 1123, 192, 1765, 530, 1509, 1172, 3312, 2025, 2872, 2944, 1809, 1716, 987, 463, 3269, 2654, 3194, 2944, 1906, 904, 633, 2175, 695, 2662, 2358, 2672, 720, 2781, 1279, 2227, 2303, 2049, 2443, 1296, 1965, 2113, 2468, 1294, 65, 1591, 757, 1164, 3166, 2137, 2708, 1248, 3093, 2018, 2280, 1013, 1610, 2916, 2591, 2842, 1635, 2816, 580, 514, 1221, 2231, 2433, 743, 1694, 707, 19, 896, 2286, 1789, 693, 306, 57, 3257, 1273, 2850, 763, 2603, 1261, 2474, 2133, 2079, 1286, 2860, 1782, 195, 2165, 2808, 1879, 1, 1951, 2754, 2700, 286, 2031, 880, 2542, 25, 2342, 1074, 3036, 1057, 128, 1079, 3282, 1918, 1609, 41, 491, 1524, 2377, 67, 227, 2073, 2509, 1439, 1160, 1490, 1222, 3251, 1901, 1490, 2225, 272, 1737, 1372, 1324, 3310, 226, 2776, 1335, 2768, 1113, 1620, 311, 1735, 160, 443, 1913, 1803, 3181, 1457, 2569, 2543, 148, 974, 2701, 1357, 2180, 1294, 1637, 1155, 709, 2124, 2828, 1059, 1415, 488, 184, 710, 2323, 205, 2977, 2645, 2103, 3014, 1927, 693, 791, 2997, 1509, 2940, 80, 3245, 789, 2218, 2282, 1865, 2319, 941, 3314, 2810, 2836, 715, 741, 1423, 2100, 2656, 3122, 2027]
e2 + mu: [1664, 1664, 0, 2, 0, 0, 0, 0, 1663, 1664, 1666, 1666, 0, 3328, 1667, 0, 1665, 0, 0, 0, 1666, 1665, 1666, 1665, 0, 1665, 2, 1665, 3328, 2, 1666, 0, 3328, 1664, 1666, 2, 1664, 3328, 1666, 0, 3328, 1, 1667, 0, 1, 1664, 0, 3328, 1, 3328, 1666, 1663, 1663, 0, 0, 1665, 1666, 3328, 1665, 3328, 1, 1665, 3328, 0, 1666, 0, 3328, 3328, 3328, 1664, 2, 0, 0, 0, 1664, 3328, 1665, 0, 1665, 1666, 1664, 1665, 1664, 0, 2, 1666, 1, 3327, 2, 1665, 1665, 1667, 1664, 3328, 0, 1664, 3327, 1666, 2, 1665, 1666, 1666, 1, 1666, 1666, 0, 1665, 1665, 1664, 1665, 2, 1, 0, 1, 1664, 3328, 0, 3328, 3328, 3327, 1664, 1665, 3328, 0, 1666, 3328, 3328, 1666, 3328, 1, 1665, 1664, 1664, 3328, 1, 0, 2, 0, 0, 1665, 0, 3327, 1666, 1664, 0, 1667, 0, 3328, 1664, 0, 0, 1664, 1665, 1664, 1, 1666, 1666, 1666, 1, 1666, 0, 1, 1665, 1, 2, 3328, 1664, 1666, 3328, 0, 0, 2, 1667, 0, 1666, 0, 1, 1666, 0, 0, 0, 1, 3328, 0, 1666, 0, 1664, 3328, 1664, 1664, 3328, 1665, 1666, 1666, 3327, 3328, 1664, 1667, 0, 1665, 1664, 0, 1666, 1664, 1665, 1666, 3327, 0, 1665, 1664, 1666, 1665, 1665, 3328, 3327, 1664, 1665, 0, 2, 1, 0, 0, 0, 0, 1, 1, 3327, 1666, 1, 3328, 0, 1666, 1, 1, 1665, 1665, 2, 1666, 0, 1666, 2, 1665, 2, 1664, 1665, 1666, 3328, 1664, 3327, 1664, 1665, 0, 1664, 1665, 1666, 1666]
v = NTTInverse(tHat^T * rHat) + e2 + mu: [567, 2988, 153, 264, 1847, 1416, 1179, 704, 1751, 1567, 2748, 629, 1628, 1915, 1370, 2802, 194, 890, 2481, 1541, 2470, 3231, 890, 536, 2924, 1024, 2, 386, 2406, 3243, 436, 1311, 2357, 2192, 2941, 388, 2216, 2797, 2590, 2192, 1442, 1890, 776, 2186, 3234, 593, 1093, 725, 2742, 2430, 2317, 2533, 3039, 2355, 168, 702, 2358, 2671, 3005, 1488, 1461, 779, 283, 256, 2641, 2416, 2212, 830, 1122, 1856, 1767, 530, 1509, 1172, 1647, 2024, 1208, 2944, 145, 53, 2651, 2128, 1604, 2654, 3196, 1281, 1907, 902, 635, 511, 2360, 1000, 693, 2671, 720, 1116, 1277, 564, 2305, 385, 780, 2962, 1966, 450, 805, 1294, 1730, 3256, 2421, 2829, 3168, 2138, 2708, 1249, 1428, 2017, 2280, 1012, 1609, 2914, 926, 1178, 1634, 2816, 2246, 513, 1220, 568, 2432, 744, 30, 2371, 1683, 895, 2287, 1789, 695, 306, 57, 1593, 1273, 2848, 2429, 938, 1261, 812, 2133, 2078, 2950, 2860, 1782, 1859, 501, 1143, 1880, 1667, 288, 1091, 2701, 1952, 2031, 881, 878, 26, 2344, 1073, 1371, 2723, 127, 1079, 3282, 1920, 3276, 41, 2157, 1524, 2378, 1733, 227, 2073, 2509, 1440, 1159, 1490, 2888, 3251, 236, 1489, 560, 1936, 1736, 3037, 2990, 1647, 224, 2775, 2999, 1106, 1113, 3285, 1975, 1735, 1826, 2107, 249, 140, 3179, 1457, 905, 878, 1814, 2639, 1037, 1356, 2178, 2958, 3302, 1155, 711, 2125, 2828, 1059, 1415, 488, 185, 711, 2321, 1871, 2978, 2644, 2103, 1351, 1928, 694, 2456, 1333, 1511, 1277, 80, 1582, 791, 554, 2284, 200, 655, 2607, 3313, 1145, 2834, 2379, 2406, 1423, 435, 992, 1459, 364]

c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
