N=6000;
m1=26196;
m2=3459;
S=[168979,2332147,34273,588782351,138435421,84761,1627875803,78593,5888731,2645278,59,1465970134,1568689,81967,24107,113923,24391,42533,45197,1329240943,141740461,153222,82729,5679871,1754094949,253399193,2917137,1023314927,1892489068,3545959,1314308018,1918132109,43759519,1027070731,267577087,848664151,178051597,14974,3869633,90863,293337809,59767079,481536953,3669269,53861,761342719,963309014,944333617,1306266121,156562577,179066,36987,79939201,2712433,1743155041,287629669,40569,948159929,728778539,62213,1481984839,2,18256842,822744847,447273802,463320811,1,1636101013,93557,3,128302,210054809,1165038079,3060418,60257,321434233,487698349,1430539547,1,378367791,154391837,125153449,1224777479,159339,1025641241,55219,1988047,44229763,1275721946,31,38733,96329,23441777,1172445583,9202178,59611,6,230271,280705053,162703249,211521,152967,1,112587,3553591,2003,1181137157,199973857,494833,58481,71741,87151,4399807,197845293,32717,968873959,59957,1,275133,491411,5756689,88789,1853993721,1509751,862402451,592188911,814409066,208224733,261582169,77933,1664526013,2751061,3217801,1052624044,90703,8434994,1672367423,95369,90823,3144641,275511,3611459,333066,49993,164014,43789,1,888036209,744167,332963843,10443,582292859,533685239,486708,12,388780643,122480499,297543,86857,241062,4632137,14537,69959,136112461,92398,7459,701853,528385723,1773703457,995098619,19531,11423,1788832183,78061897,1488720283,173840461,2644501,45817,75169,1,98145497,28559,932790283,1,792776157,1065601231,3,36097487,1477131577,612239,1305497642,831914309,3,18251,94918246,73061,42157,1595698703,3169303,183934,3293321,260254531,829075189,323696713,290679,149835649,925820321,648047909,1276463,66643,7027,1049713439,3306183,6549,554371,848364709,1492919061,1362183727,3187298,1510059763,77999,1074707321,157747039,353874,7741,197187,637966411,79043,380587399,256929,2821583,69929,356204,174651,50891,736946989,89,1,81058,88397,1407531007,1243163,22554517,5411611,1682810873,1582761363,491411,1200539293,91841,31789981,177,939221,2818666,536192354,1911445433,1105301,659441801,27529,381081,178762,237710503,120278,20483,139341529,807648041,74143,1488931337,784661737,1188734399,70177,10069058,1344691,107607,5468179,554579159,196837609,1445515087,1179085951,57587,1163393027,45622,1919211061,33880073,1583378,47148447,1,1963746563,97561,118,914516597,33613,105714617,742475931,1432049467,448479203,3374387,186856,142544863,1417877,2942057,479421,21635234,1269378718,118,98909,910264973,68749,67439419,506567,179201807,653295733,404866109,1838841526,84131,749929781,59372311,743995267,57143,685431,988564853,35967731,99817,40429,177034751,240819,220278,84121517,59,64271,2495641,1789610707,1458346063,2420059,1105259231,151238,34319,891065657,5383691,170727,868114879,87721,68276479,308423343,1323302009,83791,328197283,6310522,1,147513,3948929,413634791,230765201,431552717,1250033,5490481,1289071999,50287,39443,1,1207464211,193462,93097,1820307677,307915331,59,220144763,98493,13989,1818249767,501674963,44091793,1864078323,41957,5777693,97547,93383,10462,406338,4202806,15131,88793,271512611,261759,5891799,86269,78738053,1110247213,1072182047,162036373,1577453126,5080018,1939271,57367,1,317965573,1230537929,160774,23993,1848466999,951529,580933399,764237281,140670337,70157,2183,2437,677873143,459122269,99907,521321063,1,1,2193679,1,879680443,1,1748519387,895067039,169725553,165062,2918893,46382201,1030832731,442837687,15628097,23021,765888909,63782,4283,13537,37134677,1949496847,33113,6664107,1651791433,32183,1254664303,575129351,1271863,414444869,59,1685855159,767857997,3695701,5883333,126177209,848502481,218931,613963001,183128753,116632687,97429,863224639,69226,1958036998,33372667,1,1,2454691,84163,87959,1851739,42359479,758073769,351481762,1751832339,170717149,177,982279709,50514949,47221,245103497,94949,479614627,77041,187874263,150159,2183,4812442,1489962763,178658,1950899,19249,34290647,1,112718,71327,1967314753,1829646866,1999355387,267213,1411455082,242367,451780501,67217,178989539,834555277,5333423,1528784366,242103,320816739,1643209,1854551,70249,838829687,798467561,1833339953,807184578,10379398,194757,1892809,1141296509,39869,1076927,27744219,138754097,2,51446761,19553,1662561583,5738281,195314401,61051,1559769583,764530523,25341,972145169,228249283,1311539,1207613383,136389061,94693,257397821,4659761,2786359,9124527,1524895109,523291,214586717,1033693858,63337,2864429,33619,294339917,129754,52433,32869,16921,118930841,80073443,59,472679717,2301659,5667127,110069963,1248360551,144579,116106259,27583,352767671,787393309,678178139,36571,1628528113,420986,62143,71671,194598343,333,57529,1599902009,1557150313,1816342889,472247141,1981404001,614397397,1294283,362118,76799417,15448737,70709,140640767,1304763771,44959,2844213,59,623563207,146721086,1907764373,834877804,59,1046742761,1,52051,62366713,251331841,12931797,2414879,1840417867,84869,854080817,434202,72733,1045932749,88843,94565377,108355327,37,306588983,30259,162039,1352387,66739,239667,1848593137,167612801,83227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