L=1000000000;
N=50000;
M=10000;
D=[7586,23958,35129,35259,45639,58303,76128,94404,106418,119597,135760,150488,163383,168944,175718,192369,205702,218494,225731,228252,237790,248002,265072,274879,281306,300431,312926,332118,349704,361666,368145,371056,390253,408178,408186,423631,429749,445020,454027,473211,475949,485303,488042,494309,510992,529634,546828,562480,581748,593403,601827,605787,623962,625725,635425,636636,643529,660464,661441,671055,676990,688434,696241,696842,710941,727690,743796,744271,750592,761436,776888,785809,789716,797362,800681,818478,822095,825832,838460,854767,858271,871021,882162,894524,894905,913911,920459,930774,941185,949195,953485,954934,961688,967287,977395,992847,999087,1008630,1026866,1041598,1061283,1070271,1087607,1105661,1114868,1126142,1135514,1151890,1157059,1176239,1186154,1187136,1192679,1201216,1210721,1210937,1227838,1235723,1255306,1270655,1290392,1303803,1319576,1326176,1333676,1341879,1344278,1359019,1371759,1387260,1395663,1408303,1425483,1432922,1447820,1462086,1478376,1494920,1513237,1528665,1533576,1538963,1553626,1572706,1575416,1576553,1582664,1591058,1610036,1620346,1638238,1645227,1657034,1672285,1688923,1707432,1708921,1713982,1732349,1746317,1759656,1777986,1793923,1800149,1810629,1816288,1827737,1840884,1849264,1855043,1855736,1875058,1881436,1896528,1910288,1915927,1922883,1925350,1932360,1950225,1952941,1960908,1973455,1981815,2001465,2001750,2016247,2029135,2047775,2066011,2072206,2090025,2095884,2100630,2103952,2121385,2138564,2156876,2176075,2188856,2206577,2206662,2222247,2230609,2245223,2256141,2270491,2280426,2289824,2297719,2303430,2315940,2325250,2329970,2338061,2349480,2360976,2366581,2382198,2388960,2401773,2414381,2422977,2435682,2444252,2461459,2462758,2467668,2478858,2493829,2503928,2511918,2512094,2512120,2531956,2539098,2552510,2552797,2553333,2567059,2585429,2593679,2610264,2611786,2614267,2624587,2629080,2648850,2665575,2669267,2680429,2682832,2699640,2714679,2719121,2722208,2732030,2741113,2741656,2757154,2770238,2788474,2796605,2798294,2804876,2816705,2824371,2841809,2842134,2843989,2857532,2877388,2884809,2893279,2894739,2897311,2900479,2916307,2933484,2936422,2947895,2961677,2970165,2980090,2992478,3010661,3015425,3033268,3049248,3069137,3071459,3089416,3097358,3111263,3118272,3120059,3120348,3122515,3123458,3136644,3154480,3158772,3177814,3190551,3191597,3193091,3199095,3211310,3229665,3249621,3257522,3267778,3277283,3282984,3285199,3291392,3310883,3324683,3342588,3350773,3368792,3369581,3379341,3395687,3412116,3417750,3418513,3437715,3455162,3472174,3491597,3508306,3527389,3528042,3530138,3545353,3561571,3569031,3578707,3596238,3607363,3611242,3618179,3623796,3627934,3642011,3658413,3671283,3673944,3692232,3692730,3696136,3702056,3709800,3717315,3730594,3735118,3753539,3762853,3780279,3788660,3789075,3791103,3799540,3811622,3821726,3835032,3839982,3847493,3857808,3867568,3883056,3892000,3893155,3894226,3894915,3914582,3931093,3937978,3945472,3955309,3970875,3988978,4007504,4026032,4037054,4050711,4067813,4078497,4096305,4115383,4128134,4137600,4144554,4164110,4176947,4181318,4187915,4205458,4220421,4234432,4238358,4241226,4257017,4267109,4267172,4269632,4284389,4289477,4300948,4305232,4324930,4326559,4333744,4342150,4355229,4373376,4376953,4391750,4401990,4412349,4423639,4439052,4441804,4458334,4465574,4484375,4489980,4492926,4510127,4517358,4518705,4530724,4548500,4549536,4565106,4566470,4571704,4588249,4592699,4595892,4600356,4614391,4628033,4635895,4650559,4666920,4672717,4680913,4694413,4702807,4711908,4717467,4728726,4744886,4747261,4765657,4782340,4797316,4814857,4831799,4837716,4845246,4859104,4878285,4892752,4909500,4911052,4920126,4937776,4950734,4965771,4979245,4989808,4994453,5010404,5029118,5040606,5052996,5066617,5069979,5087757,5100242,5111425,5129175,5131504,5141479,5152017,5167935,5172967,5179844,5190843,5195973,5212843,5232250,5251816,5271135,5273082,5290480,5304227,5309523,5314698,5332572,5345606,5356327,5374804,5390307,5393476,5395279,5413849,5424062,5434801,5449005,5456707,5459795,5464816,5465532,5485462,5501855,5502893,5511785,5517720,5536682,5553812,5567708,5574632,5575167,5581377,5600512,5612801,5629297,5648148,5663306,5671649,5679647,5684158,5685691,5702602,5703061,5721784,5728803,5740470,5754133,5759266,5767599,5774545,5788434,5807203,5808184,5819998,5836484,5844700,5857402,5865230,5882874,5901771,5914949,5922225,5924793,5927413,5937255,5942184,5946052,5947917,5949628,5952260,5953220,5966387,5983469,5984473,5990415,6005698,6019804,6028967,6034353,6037151,6047316,6052805,6071503,6081715,6087516,6098751,6100860,6118152,6130353,6141020,6148594,6149357,6156349,6169476,6170831,6175688,6193030,6193548,6197483,6212825,6219582,6237760,6241850,6261162,6268937,6285137,6290620,6301519,6304555,6309483,6319946,6326383,6345824,6365149,6383612,6384905,6395020,6406852,6415812,6422099,6440709,6454281,6467750,6481440,6492990,6501144,6517888,6535892,6551909,6553311,6557627,6572118,6585592,6587507,6589500,6592114,6604964,6622025,6638351,6652755,6665733,6680390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