n=1000;
m=1000;
r=[3,4,6285640,6288442,348276846,503924960,503924965,503924965,503924969,504230439,162242037,162242051,162242061,162242061,162242063,162242085,162242086,162242088,166147064,166154949,166154955,166154955,198753134,198753137,198821447,198821447,198821454,198821454,198821461,198821990,198822011,222266954,222266958,222266974,916729920,761081809,761112706,761302157,761302167,761302167,761302171,761346579,822695531,822695541,822695541,822696565,822696565,822696570,822696583,822698959,822698962,822698965,830116294,978864158,971446981,971447036,971447042,971447114,971447116,971835288,971835295,971841679,971848619,971848622,971848625,971848627,971848627,971848682,971848689,973252082,911903200,999998842,999998843,999998847,999998850,999998871,999998875,999998875,999999970,999999977,851252210,851252214,853398459,853398461,894202351,894202356,894202359,854335298,854335299,880642210,960308647,960308648,961008055,965659371,965659378,965993062,965993064,966000579,966000529,966000541,966000543,966000543,966000549,965999457,965999470,965999473,991022685,991269427,991269428,991270493,990965034,991034397,991034400,991035162,964728254,964728255,964728257,964728257,964728258,964728434,964728437,964782946,964782950,964842265,964842274,964842274,964842260,988046132,988039264,988039267,988039290,988039295,988039297,988039298,988294794,988294272,993580002,993580004,993580004,993580011,993580012,993580012,993580013,993580014,999999992,998596515,996595059,996595072,916928640,916964009,916964017,916964019,916964021,987346166,987346166,962322963,962322964,962322968,962322970,962322976,962322976,962322979,962322983,938878049,938878055,938878057,943971345,943034528,944572114,944572114,944572114,944572116,944536641,944529129,944529129,944273652,944273654,944273656,873322776,865078922,865077318,865077630,973741593,984346084,984346085,984346086,984346090,999409301,999409303,999408920,999408923,988804433,988804434,988804446,988804448,984911885,984913894,984913894,963711497,963711497,963711499,963705119,963704103,963704104,963704107,963701739,963701746,963701750,963701752,963701754,963701755,963701774,963701777,963701777,931103601,931103603,931103603,931103622,931103558,931103558,931103560,931103560,931103561,931380646,926094922,926094905,926094878,921443574,921443581,921443486,914871884,914871884,914871879,826776258,826776459,826776439,826776443,826775696,999951932,999950220,999950218,999950227,999703492,999703492,999703492,999703496,999703499,999369819,999369821,999369824,999250463,998932643,998932651,999999989,999964569,999964574,999255323,999964578,999953277,999953281,999953283,998885941,998958687,998958690,998946232,998901655,998847540,998847540,999627153,999627714,999627718,998848107,998571027,998571028,999999298,999999298,999999302,999999302,999929939,999929766,999929769,999929769,999870514,999870525,999870527,999870534,999869471,999869456,999867393,999867731,999867737,999999991,999999969,999999972,999999660,999999661,999999662,999999725,999999725,999999726,999999785,999999908,999999911,999999919,999999919,999999920,999999919,999999921,999999921,999999924,999999932,999999939,999999943,999999868,999999918,999999919,999999919,999999922,999999924,999999930,999999945,999999961,999999955,999999969,999999968,999999975,999999979,999999979,999999982,999999962,999999941,999999957,999999958,999999996,451527386,451527389,558760073,574890429,574890426,695207206,695199324,695199195,701168808,701168805,701168809,701168801,701168801,717198694,717198694,717198694,717198959,793454345,793454353,793454352,794323379,794323388,794323877,794323875,851035981,851035982,851035992,851036055,851154488,851154491,851154492,851154486,731963107,731963103,731963101,777774439,777774431,836205656,836205655,973603408,973622899,973687753,973687756,973687756,973687754,973728251,977143413,999860639,999860639,999860615,999860615,983834021,983834020,967703682,967703681,967703683,967703683,967703683,967763491,967763488,967763491,967763495,967763498,967763506,967763517,967763510,967645087,967645089,967645081,998343498,998278643,998278651,860881336,860881341,860881332,860881317,860881319,860881319,860881327,860881330,860691869,860691870,860691866,860691881,860691884,860691884,999999983,999999999,999999996,897468362,790235678,790235678,790235675,791509002,791508989,791508989,791508988,791509128,791509125,791509127,792277594,792277594,748818895,748820042,748820042,810491132,671196106,671196106,595963852,595963857,595963858,595963852,592548771,592548773,592548840,592548839,592548839,779520125,779520128,779520134,781852756,781852756,784594189,784627126,784627137,784627130,784627130,784627128,787537003,787537062,787535869,787535869,787535872,789862791,789862790,789862778,789862782,789862776,789862757,802575981,802575990,802575995,802576004,802576008,847783304,849754322,849754326,662785735,662785721,662785721,662785720,662785730,662785730,662785730,662785732,662785726,662785725,666137310,666137310,666137308,666137738,742004195,748782979,748782975,748782976,703611386,703611384,7036113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