constants.py

data_range = 10000

a = [93813, 72462, 54256, 86601, 90873, 61243, 86252, 66142, 67779, 83993, 55574, 79772, 97415, 63851, 54312, 78453, 71252, 52683, 55672, 71310, 76641, 53061, 66546, 99670, 86486, 70515, 71668, 83430, 58962, 76965, 98616, 88623, 56565, 76716, 60462, 87046, 77098, 85355, 97562, 90964, 99944, 50525, 80483, 57215, 66786, 99495, 53850, 95260, 75516, 52163, 63782, 73657, 64077, 58992, 85169, 86684, 50100, 87680, 78268, 98019, 74746, 54712, 71854, 56210, 89243, 53473, 76703, 81684, 52569, 65047, 68777, 87928, 66084, 87043, 100849, 98593, 77568, 72180, 76667, 94278, 60307, 68749, 93760, 99169, 71126, 83453, 77219, 91133, 100071, 80694, 93453, 65379, 86967, 89736, 58753, 58437, 88402, 62595, 98527, 96300, 88751, 56281, 79191, 87069, 50107, 68392, 76440, 88397, 98477, 82220, 74044, 70007, 59142, 99293, 68463, 75260, 63064, 90901, 71173, 73912, 85066, 100930, 50060, 50265, 90671, 90519, 88677, 78396, 83021, 87526, 87053, 80892, 64430, 66392, 87320, 62975, 82267, 59593, 52963, 87343, 69893, 89993, 67425, 99318, 59804, 63043, 63308, 53704, 61624, 67614, 64998, 58390, 95164, 89632, 53668, 64030, 62733, 85435, 63654, 69824, 81818, 60119, 59087, 69272, 50712, 90488, 56732, 77062, 77327, 96509, 56920, 60756, 91269, 55874, 56486, 68403, 68347, 86612, 90559, 87626, 100472, 63704, 58142, 57261, 58053, 69119, 59731, 78473, 85373, 75073, 56817, 98784, 58214, 56161, 89382, 57975, 72746, 91050, 75560, 50339, 53660, 67254, 50956, 90288, 53322, 95067, 82710, 56295, 63205, 82863, 67515, 85035, 56015, 66805, 85771, 54930, 60443, 91091, 95929, 61349, 56534, 100335, 80083, 54773, 89191, 61291, 51273, 66088, 59592, 68833, 85104, 98548, 91278, 88325, 99731, 63420, 80131, 71322, 85654, 69734, 69255, 62269, 60154, 94031, 50597, 63897, 82689, 57449, 69891, 91663, 65744, 75069, 95931, 88723, 69759, 50408, 90625, 80007, 50851, 54560, 73534, 72944, 61655, 56507, 91365, 51066, 95893, 81226, 60603, 53133, 51140, 100119, 87189, 54172, 95892, 97999, 87944, 73031, 74150, 61704, 72842, 85204, 52017, 90707, 58203, 101334, 60391, 72489, 52229, 99387, 89385, 56355, 58653, 98293, 85161, 75444, 75897, 89886, 73056, 69725, 69564, 54783, 88078, 71834, 54133, 79532, 52553, 60156, 59952, 66155, 83442, 89892, 54000, 69472, 76220, 95230, 89860, 53754, 88276, 59554, 68477, 70426, 79475, 63069, 52766, 95982, 79530, 91633, 77890, 57685, 85186, 79613, 65271, 55997, 50289, 96988, 82444, 53645, 69928, 87375, 100592, 89009, 67683, 71175, 69265, 61385, 86522, 95430, 90147, 72848, 71989, 60044, 94883, 68338, 73018, 88490, 78487, 87753, 52048, 63058, 85675, 58275, 98679, 81023, 63469, 88268, 65521, 93620, 94883, 100826, 89545, 100618, 94313, 72352, 69753, 53217, 68426, 53929, 53264, 89691, 50050, 95725, 69968, 75627, 80415, 80651, 98464, 74378, 90946, 61727, 93870, 53561, 71635, 69660, 65458, 63501, 76348, 86540, 55578, 57280, 99836, 68173, 85418, 88509, 97847, 53164, 58349, 56316, 67517, 64675, 86464, 63854, 71720, 53264, 83083, 86217, 100492, 92802, 101666, 99572, 92411, 76996, 69532, 86668, 53666, 70383, 71643, 64101, 90830, 93438, 86605, 80865, 55301, 80635, 70856, 66975, 64545, 55676, 93728, 51037, 82855, 87098, 78234, 97647, 100800, 90666, 88378, 84766, 66817, 52563, 93564, 64216, 70795, 87153, 91042, 80206, 79374, 65814, 57025, 73120, 74722, 72325, 93429, 68098, 54017, 80559, 101165, 76681, 77579, 82070, 85296, 50085, 84211, 80102, 91227, 50338, 69048, 97604, 85968, 65956, 88423, 85313, 76637, 81369, 75454, 94818, 94427, 94061, 90556, 55860, 74887, 81451, 88540, 60448, 90948, 52105, 75138, 92351, 75458, 81462, 60717, 101023, 67964, 51075, 78246, 53693, 66673, 78443, 74287, 68212, 96782, 82502, 84626, 59905, 80666, 97922, 54446, 89018, 77764, 72382, 71843, 81179, 96653, 60464, 69222, 62895, 71695, 99583, 87749, 59255, 81170, 76442, 70863, 76097, 61033, 90765, 84061, 71735, 85023, 52549, 98338, 56398, 60229, 66838, 92226, 97044, 81409, 95200, 65954, 98371, 57865, 72638, 66865, 87055, 50852, 85985, 74352, 90607, 62381, 97259, 57923, 101202, 66252, 78158, 56816, 89218, 91390, 61936, 50577, 70242, 60114, 50284, 67707, 75403, 63435, 82661, 56948, 52535, 80024, 95468, 76566, 83890, 91974, 90521, 66469, 87198, 67806, 97296, 80009, 95848, 94120, 57717, 73123, 79914, 52824, 85899, 80225, 56281, 61554, 92131, 70561, 93177, 73423, 87757, 96173, 59484, 93853, 100743, 77558, 75688, 94898, 62158, 58899, 84796, 65568, 98694, 83341, 100347, 92267, 69350, 55243, 76721, 57335, 67048, 70202, 80428, 82612, 78096, 101074, 64922, 66689, 68151, 64146, 60525, 92478, 74974, 50513, 77923, 96948, 96352, 54511, 68462, 80972, 66265, 55389, 68797, 97664, 94517, 65992, 58760, 82005, 72654, 65271, 71545, 84692, 77052, 65148, 62531, 75624, 72074, 51512, 56530, 68935, 91402, 94039, 82590, 66712, 51614, 78269, 79932, 54350, 75598, 56635, 90303, 79532, 52136, 61616, 62917, 50259, 86650, 73398, 87333, 92305, 51940, 99727, 94760, 94326, 96546, 91234, 94950, 60211, 62148, 78192, 67820, 86843, 86839, 93515, 52083, 61278, 51051, 67834, 86888, 58508, 56924, 86748, 52146, 55605, 83399, 92531, 89119, 70053, 75290, 51695, 80638, 87312, 78375, 94861, 71116, 72767, 89533, 70507, 61124, 82802, 101137, 99084, 56685, 51171, 94993, 88983, 61094, 55586, 69407, 94173, 55029, 76693, 79245, 100892, 70147, 70821, 78334, 95721, 55974, 79400, 63905, 68468, 64071, 58909, 76853, 77002, 89691, 50767, 61017, 79400, 51308, 89553, 51794, 90529, 56242, 51456, 74311, 74377, 99025, 89907, 62872, 100794, 62524, 98594, 60089, 58597, 95475, 59546, 93149, 76519, 93538, 92409, 96574, 78313, 75419, 61820, 100151, 75260, 70098, 94996, 66204, 50139, 88675, 90728, 73189, 50291, 95512, 70300, 62368, 70365, 61021, 89403, 87162, 93728, 65897, 64122, 92722, 75943, 88713, 54568, 60219, 68123, 72546, 57824, 88543, 95061, 53912, 86477, 99155, 84518, 90930, 59057, 97629, 97692, 71400, 77944, 67360, 50061, 89653, 55762, 77307, 67979, 55283, 62272, 86014, 91641, 78107, 100499, 100473, 72886, 61047, 89743, 66937, 90801, 70445, 77972, 55984, 54335, 68499, 89631, 92018, 67580, 50175, 90252, 90296, 94050, 91372, 95992, 78539, 59513, 63540, 61800, 98857, 88756, 92794, 84503, 85586, 82623, 96516, 89312, 87782, 63597, 90146, 81097, 79438, 71553, 74720, 74578, 77666, 75805, 96261, 100325, 95200, 70247, 98813, 98297, 58367, 73090, 93532, 82584, 55256, 62951, 89470, 55424, 57312, 68144, 81107, 72111, 52734, 95527, 67918, 50031, 98024, 92814, 96383, 84933, 91213, 73431, 94547, 81061, 70517, 84462, 51534, 58822, 95844, 92127, 94692, 97233, 67904, 89911, 76114, 81467, 61539, 87210, 65437, 70744, 95236, 67578, 100758, 54726, 85385, 68582, 51509, 93665, 63252, 95742, 101590, 71064, 96096, 63860, 92368, 74412, 54428, 52753, 80450, 61685, 84831, 51867, 82619, 75303, 73022, 92621, 73887, 87007, 63577, 61892, 100906, 90421, 60534, 52766, 72894, 89695, 64783, 52108, 96973, 86218, 76725, 71017, 54303, 58723, 92826, 72225, 97667, 73874, 67488, 89709, 89911, 65569, 99281, 90444, 58503, 79514, 63436, 87554, 62460, 65406, 58900, 92881, 92914, 64735, 81953, 82602, 92803, 83666, 85780, 92209, 72327, 95780, 78808, 82692, 90763, 58471, 76815, 68548, 81868, 90332, 53957, 77352, 88985, 63321, 86662, 85622, 64814, 79867, 79665, 55755, 87735, 67729, 70862, 68734, 96358, 61546, 71654, 64200, 72973, 92360, 51357, 71130, 88640, 72095, 86305, 88803, 98903, 87291, 77808, 80529, 95948, 82695, 52820, 79323, 71969, 70287, 91401, 81335, 82494, 64441, 81152, 60342, 71935, 83665, 94748, 61331, 59121, 66996, 93091, 79787, 90591, 61586, 85523, 89170, 62412, 90335, 77036, 56008, 73578, 65195, 61025, 91475, 83594, 88925, 63422, 98385, 94394, 92561, 99461, 99387, 100383, 66060, 94040, 90648, 77440, 84847, 73455, 99852, 55886, 88637, 64758, 86624, 78702, 65133, 94478, 64652, 76007, 53558, 98601, 55994, 73943, 69711, 87075, 84334, 50257, 83790, 100593, 54793, 88011, 62551, 58934, 56464, 88833, 54989, 96279, 72608, 96535, 79016, 86740, 85611, 84163, 82457, 95359, 79372, 70836, 60452, 59285, 71102, 68731, 98306, 94306, 80241, 59148, 86017, 69400, 53396, 88945, 73348, 75156, 97182, 73766, 95045, 64082, 66698, 55407, 85048, 83412, 70096, 62471, 66179, 70449, 60789, 59629, 89285, 53566, 74842, 50894, 74081, 81430, 90331, 70229, 89201, 75113, 100122, 51251, 95289, 94339, 98769, 55452, 52750, 91683, 51739, 57547, 87629, 94639, 61726, 58107, 78629, 99289, 81967, 63199, 93444, 88256, 77348, 76342, 90928, 80438, 55924, 97443, 62989, 86210, 74633, 93229, 100859, 71407, 82405, 58929, 74696, 59972, 64808, 63513, 71251, 70126, 82168, 93221, 53609, 91922, 86002, 63819, 89411, 98173, 96174, 79986, 85323, 85110, 89397, 61480, 95629, 82244, 53563, 89313, 68631, 64444, 56078, 99972, 99866, 64020, 57352, 65625, 84996, 59326, 91620, 52098, 92486, 88128, 56993, 56592, 77102, 77470, 62879, 50833, 97659, 101553, 100268, 88046, 84830, 79584, 68751, 85028, 68036, 95557, 83365, 56437, 93923, 71606, 64169, 92212, 89421, 61836, 77115, 79373, 52182, 88329, 69444, 52553, 61079, 76237, 87695, 61842, 73153, 59989, 101276, 77542, 64833, 67350, 88841, 99334, 96357, 78921, 64357, 53816, 95450, 67433, 54016, 56822, 85086, 68836, 59559, 54184, 89572, 100828, 82875, 63013, 76179, 82929, 64050, 59102, 99810, 72829, 87830, 89160, 67683, 87198, 95310, 100652, 57529, 71978, 54767, 77859, 87443, 100674, 58484, 61772, 52961, 88223, 96293, 76056, 69035, 57360, 55661, 75976, 86601, 52863, 50789, 74981, 54440, 90413, 75735, 94273, 83860, 88813, 72973, 94879, 52433, 53379, 89971, 99193, 99613, 68195, 97340, 84336, 51812, 74230, 75371, 91354, 97842, 79376, 86153, 71684, 97943, 73132, 74100, 68701, 57062, 86147, 61533, 53389, 78207, 65955, 55670, 90337, 55169, 54964, 85947, 66801, 71927, 50309, 54299, 96903, 95833, 97538, 82259, 51647, 84776, 80910, 60341, 88069, 73735, 97975, 84840, 68921, 57220, 77622, 55864, 83932, 85846, 99207, 77022, 56102, 99948, 94702, 88031, 88333, 55503, 50896, 84128, 76372, 70990, 54157, 68989, 56415, 70377, 99989, 99947, 68283, 84463, 99752, 71604, 54898, 86752, 95244, 78809, 91580, 58852, 50612, 93289, 94356, 54582, 90988, 88339, 86308, 83229, 96694, 64478, 73580, 97961, 86211, 91095, 85058, 71303, 90013, 98569, 63393, 90138, 70230, 60726, 59553, 70614, 52707, 73300, 54995, 78317, 100761, 69124, 74986, 84530, 101046, 93451, 54602, 81314, 55749, 100120, 54451, 72436, 70780, 72878, 50980, 65151, 78550, 88644, 63188, 69006, 92406, 52455, 80613, 56724, 91929, 76945, 80566, 100406, 69176, 83524, 85842, 66916, 77174, 52716, 58711, 61985, 88509, 95194, 100901, 72981, 93723, 76930, 62539, 73783, 97182, 100518, 69680, 98480, 53456, 70738, 55472, 84833, 50615, 72341, 74947, 85488, 74470, 86765, 99128, 56554, 75799, 66767, 77998, 65356, 62196, 81733, 68042, 68853, 51509, 88724, 69817, 60531, 76603, 101632, 92010, 55079, 98948, 53186, 64569, 93507, 94343, 81473, 90669, 76441, 100711, 53352, 74126, 80957, 55439, 53553, 84356, 51731, 50598, 55017, 57772, 71129, 54110, 81392, 55040, 71669, 76919, 58301, 61873, 95340, 94840, 63183, 77468, 71119, 101114, 92730, 73799, 61707, 51296, 87907, 85621, 55258, 56393, 101580, 86665, 60268, 80843, 56709, 76487, 59469, 73285, 95238, 91279, 78799, 54452, 82757, 73964, 78776, 101428, 97246, 85619, 63975, 61160, 62414, 64153, 95832, 64869, 66108, 78251, 76473, 81545, 57195, 92571, 101507, 94683, 71840, 76076, 74831, 86074, 64599, 63406, 80319, 83530, 65533, 60031, 63244, 81087, 51234, 65033, 98127, 74629, 88027, 98057, 89125, 90520, 84400, 63048, 57110, 99186, 52507, 61211, 52016, 74854, 62738, 71134, 61887, 63319, 81551, 85233, 98175, 64393, 75651, 68230, 98840, 67435, 75675, 53480, 53192, 85849, 84031, 94278, 70856, 88582, 51874, 87504, 74969, 56421, 88392, 59259, 50211, 55325, 73943, 83699, 52343, 89665, 53852, 81025, 94467, 77889, 64189, 72742, 52178, 71812, 73279, 74189, 72782, 72185, 81013, 84548, 69678, 84489, 69138, 58003, 57574, 54193, 90978, 73693, 84976, 85004, 72023, 82353, 93220, 84827, 95100, 88433, 87041, 62697, 63560, 81366, 95196, 58737, 68349, 79522, 85473, 69284, 72720, 58409, 70502, 59944, 65718, 53639, 71186, 80313, 66856, 89387, 58301, 98692, 61765, 68064, 70534, 83120, 70678, 81199, 91529, 67383, 78287, 87334, 67602, 69208, 83023, 66509, 54118, 77324, 51381, 87625, 90108, 51842, 91139, 60776, 53572, 93231, 82200, 65025, 76279, 50753, 76227, 82473, 60570, 101081, 81586, 74664, 64396, 74136, 56466, 87111, 63030, 66636, 98166, 83466, 94991, 67696, 69671, 97733, 89923, 99624, 81809, 57113, 61992, 80549, 70019, 62884, 59230, 73550, 94497, 67127, 80107, 96206, 73205, 94665, 99349, 59358, 56804, 71217, 87061, 92892, 58745, 71407, 69385, 94743, 89733, 60055, 92896, 71114, 57209, 72631, 89729, 101557, 98618, 82133, 53548, 98110, 91251, 95919, 86376, 52700, 101111, 89004, 68639, 72541, 57553, 57323, 91985, 55112, 51791, 91015, 98248, 88430, 93438, 51223, 51458, 87339, 82007, 80437, 81684, 82745, 61108, 67788, 76063, 51189, 62824, 90809, 67044, 77432, 89927, 64524, 60070, 90816, 70190, 60467, 63912, 71485, 101101, 90324, 82532, 81544, 79997, 50937, 66761, 61165, 64327, 58432, 85074, 93501, 61648, 97291, 95840, 65834, 67501, 65283, 66499, 96542, 56558, 64507, 64066, 101128, 53578, 78122, 53938, 87371, 56155, 64987, 60593, 69595, 56746, 100647, 89237, 99358, 63188, 59981, 82928, 57483, 81062, 71383, 51973, 91945, 70444, 79173, 64797, 55210, 75800, 53780, 59463, 99513, 73018, 56220, 72693, 71777, 67485, 80103, 57575, 72343, 94387, 83323, 76493, 74936, 83886, 54227, 70694, 50552, 81611, 99594, 52345, 79718, 84739, 97001, 75778, 97218, 79014, 60718, 71178, 55055, 90685, 68907, 79815, 80620, 67870, 57759, 56352, 91506, 83446, 60269, 90668, 69410, 90961, 81230, 91022, 91350, 64457, 98015, 66739, 83375, 89232, 59431, 93210, 92621, 94954, 56409, 58266, 75838, 98547, 57372, 79960, 94830, 89133, 70936, 67114, 53867, 67948, 91697, 76191, 80081, 50104, 61632, 78322, 67650, 100122, 93286, 70044, 83550, 76957, 81656, 89744, 86224, 61440, 98254, 95767, 56665, 72953, 98350, 66602, 71016, 85936, 66149, 78717, 83850, 69947, 95621, 66622, 101563, 60359, 88308, 65811, 56016, 71903, 95710, 75065, 71725, 71631, 85330, 58215, 92739, 86757, 85849, 74257, 63063, 55475, 99721, 92266, 61607, 101455, 63812, 59196, 86441, 77306, 52406, 70542, 69430, 87268, 78868, 83933, 67692, 65273, 90436, 53122, 67321]

b = [100220, 90438, 83854, 66904, 65117, 68546, 55063, 99934, 82071, 98100, 93964, 92357, 63961, 80154, 87835, 78153, 97687, 69133, 59274, 82383, 84562, 86378, 100519, 60869, 82177, 91549, 57911, 92069, 73649, 85851, 56893, 72113, 72110, 99601, 59026, 57730, 51563, 69036, 71431, 86928, 61300, 82644, 87450, 89495, 97664, 61317, 83036, 86948, 66324, 58521, 79829, 64695, 91939, 85662, 87348, 76618, 96342, 96237, 75042, 94616, 94981, 80595, 93923, 64243, 68299, 84703, 60118, 71994, 85102, 85356, 64544, 71958, 99241, 85475, 63360, 55656, 50020, 73484, 85282, 86393, 70539, 59516, 77204, 63898, 94831, 90401, 86671, 97333, 71673, 95800, 55827, 94981, 59765, 89829, 94447, 81924, 77900, 85395, 89030, 75089, 73229, 57083, 101002, 79739, 65185, 69990, 80768, 56755, 96952, 91777, 70769, 82143, 88971, 62647, 84243, 53390, 56905, 76420, 76991, 54325, 74676, 53008, 69120, 71020, 65966, 88324, 90320, 56945, 81798, 92083, 100358, 58839, 88843, 93737, 51087, 68329, 85746, 63101, 97879, 91449, 72620, 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