N=100000;
M=5000000;
Q=0;
u=153252866;
v=506034425;
t=51;
A=[9865456,7275647,9260296,4104264,5535150,462208,1644763,689101,7363715,1033468,31742,8117855,9405123,9678832,1049835,7137478,2716406,7268943,6840016,5927980,5324650,8365832,6679771,4607288,8319786,8112205,7511041,7448233,9133758,6866349,6360712,9733318,7564235,9637206,2025350,3120047,1043242,1285522,4774976,4779339,9104490,4304968,990254,6434215,3582550,8921070,2993800,486579,4905816,6996722,9418546,7369188,8419338,115986,4871651,2861256,5477984,7227778,7487852,3818521,1725248,9915365,2902786,1285557,568350,8123221,8224911,7218062,7220990,7074851,5710376,4911952,9527263,9529251,8395989,329247,4091444,8724822,2709953,970787,6804176,6988872,4834927,6739814,1223127,6731932,5504090,2488052,4927928,3726395,8746879,3515660,8926553,1904537,3607886,7622241,8679395,1044880,7692804,9378097,3239956,2333059,7232638,2742206,3169711,8659506,5593701,2650259,4839451,7103883,330922,1305267,4107367,6549537,4977253,1688783,5027386,3480113,8511699,9713772,9749218,5455534,3174802,7765043,1896556,1971693,5859878,2549796,6167943,9760596,727973,5725467,4995110,9643369,7851066,9296410,7846107,4179583,331594,582468,1687361,7832449,1684193,3674531,1980614,5546285,4911911,2977781,4203471,2743594,4556348,4073880,2392494,2150280,6865144,2228273,9873771,3461492,5122253,6466981,253485,2614320,3389764,7916510,5399731,9734160,2765596,6164290,8290736,1784388,3437862,6874879,2317307,8891548,9418962,9503060,6152566,766692,5432915,4481247,2624851,2436460,7379903,9376213,5937359,5334293,5380767,8065213,3984312,5380687,4971624,6856400,7657627,1062770,2366476,5851023,381556,6479340,551068,4372156,5961281,3925001,8918989,8712708,40743,7797091,6813379,8327727,9271882,1980022,9024549,768119,4662883,4843470,193569,7476192,416190,8517144,1171778,1002999,9757743,7299455,7162533,6731683,9472648,9609882,1168117,4894293,9144919,9349372,181904,8059073,5493724,2554614,3894217,2684978,7638471,6304590,6582175,7995136,5809290,8555955,6513595,9454556,1608933,1653192,382624,8505473,8875823,1997340,9801043,8427009,2094664,4613902,2787795,7284385,6096332,3486850,6384685,1204403,7617554,2185393,167407,9410959,8476822,6448125,6144519,2136888,9581560,8188241,8229019,1718340,2155168,4005470,6675390,7560524,4158178,1343134,1158273,1901216,7541381,542371,7427616,9740562,6524639,4344872,6085750,1528133,1104758,7197614,4108290,3953889,8647206,2006838,5838588,2665184,9546554,8751108,6465317,9981282,8618041,7752891,628618,7311177,263680,1407196,3914592,2702180,9860269,3150835,3745814,3987824,9492466,4450747,9614362,2394567,4141017,1790169,8149214,556180,8670197,2231653,4703414,5428047,710946,2589308,5573676,8749752,6451657,787793,5154148,7046787,8059372,9899581,866379,601570,9107303,530396,3428660,9415696,9377612,8070368,7581969,7911405,986972,7199268,8745851,8341683,4247844,359988,6958243,1254943,6110443,6932925,7938348,4930485,4238258,3468802,8445398,5578210,7635365,5605454,6813689,2471765,1911502,5256976,7849779,6821253,4349149,4486467,7072919,1641046,7743291,1564785,6375833,2545695,8780682,377130,450483,6257968,7971239,5319368,3540117,7234240,147100,2594303,501393,8488215,7640675,8519227,2930289,1594764,879181,2077290,5417658,7084845,9711405,5017170,1115253,1765383,7412728,3077440,2495858,3816098,1910766,5853313,4465458,8553007,1713590,3719420,854548,481573,7099044,12967,5973197,9023899,7999661,7658047,2128073,5306542,3798711,8468964,4359359,4778499,786318,2058190,4343580,3733334,9141209,3485010,7086480,698460,1510120,3058124,5392823,9946363,6847584,2657285,8207580,4708771,4057681,5040848,1844728,3528579,208044,3447540,5350296,332043,7713182,9740851,9441153,3994580,8672870,9610181,4918091,2282932,8978302,8064770,8855861,5860733,6094472,1819819,5267129,1997744,8032068,6845421,9605050,662453,9572741,552515,8165766,548452,812930,1559932,9449007,9802674,9118853,5324334,5844222,1655734,5347542,7153903,2274458,1241067,5209200,5253363,6163010,5796098,25575,5824704,8524774,9990532,737127,4457519,4597443,8312867,6514472,8579269,860651,3711600,7635887,4870984,8147416,9847120,6284090,7349666,9361320,4238197,2473787,8359052,6063988,379274,2492906,5128400,7250756,1847865,5528185,6690315,345135,3794969,1775180,7756304,4905772,9598997,3831293,2459127,2097292,1795570,1991485,7033158,4193248,6081003,9117326,479554,1232663,8234678,9180084,5952390,3966239,2463989,1995158,8412920,2797271,9581828,5274691,4426563,7880054,2536480,2575875,9715317,2697174,6676892,2572044,9587246,5052565,4853030,1932256,6518848,2965206,3903105,290060,6281489,364084,2903019,1632245,2775742,4937858,8326583,6387766,5084508,8761093,5672676,2616335,4525459,4587551,422181,5381364,3988538,7076168,5690512,2280005,1845689,5437377,9209892,263208,6285176,6680586,9327204,4609755,1537720,4188285,463393,6542656,8839471,8148499,1230386,2068568,269824,9924872,817911,4099493,2030077,3777724,5816912,6092395,139635,5640400,5881197,8872804,4609312,8349106,6708012,4887,6359148,3896753,6692647,3193602,1093970,3298433,5770523,5738668,1787826,4739543,417119,186866,1330837,5791168,8646494,5459378,8424854,2452134,775149,9202121,927626,6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