King’s Game

题目连接：

http://acm.hdu.edu.cn/showproblem.php?pid=5643

Description

In order to remember history, King plans to play losephus problem in the parade gap.He calls n(1≤n≤5000) soldiers, counterclockwise in a circle, in label 1,2,3…n.

The first round, the first person with label 1 counts off, and the man who report number 1 is out.

The second round, the next person of the person who is out in the last round counts off, and the man who report number 2 is out.

The third round, the next person of the person who is out in the last round counts off, and the person who report number 3 is out.

The N – 1 round, the next person of the person who is out in the last round counts off, and the person who report number n−1 is out.

And the last man is survivor. Do you know the label of the survivor?

Input

The first line contains a number T(0<T≤5000), the number of the testcases.

For each test case, there are only one line, containing one integer n, representing the number of players.

Output

Output exactly T lines. For each test case, print the label of the survivor.

Sample Input

2
2
3

Sample Output

2
2

Hint:
For test case #1：the man who report number \(1\) is the man with label \(1\), so the man with label \(2\) is survivor.

For test case #1：the man who report number \(1\) is the man with label \(1\), so the man with label 1 is out. Again the the man with label 2 counts \(1\), the man with label \(3\) counts \(2\), so the man who report number \(2\) is the man with label \(3\). At last the man with label \(2\) is survivor.

Hint

题意

有n个人围成一圈，然后开始报数。

第i次报数报到i的人出列。

然后问你最后出列的人是谁。

题解：

数据范围只有5000，所以直接暴力离线打表就好了。

我写了个暴力，然后跑了大概500s，然后就把所有结果都跑出来了。

代码

#include<stdio.h>
#include<algorithm>
#include<iostream>
using namespace std;
int a[6000]={0,1,2,2,2,4,5,4,8,8,7,11,8,13,4,11,12,8,12,2,13,7,22,2,8,13,26,4,26,29,17,27,26,7,33,20,16,22,29,4,13,22,25,14,22,37,18,46,42,46,9,41,12,7,26,42,24,5,44,53,52,58,29,22,12,48,27,30,58,52,49,57,13,14,32,24,75,8,67,56,40,61,51,77,35,57,74,63,75,12,72,89,11,32,32,59,61,62,89,22,31,67,33,101,101,34,74,90,89,61,73,18,26,72,96,25,53,93,42,11,80,42,94,32,80,12,7,97,22,82,119,94,88,60,123,88,119,76,128,34,116,57,140,103,133,107,44,100,53,20,51,12,74,59,146,111,13,119,39,9,142,31,154,99,26,5,99,110,135,155,99,86,2,8,49,16,126,149,76,123,101,168,128,94,51,38,107,119,70,64,149,4,62,94,99,61,2,39,164,149,73,109,83,81,169,26,181,166,109,140,89,64,62,94,30,168,27,31,192,82,215,7,184,199,158,198,215,62,157,58,18,51,200,57,226,2,236,50,106,188,22,128,149,162,206,228,150,26,205,18,9,107,68,188,165,184,238,48,95,92,62,143,164,238,156,64,86,134,130,245,258,252,62,191,138,71,243,102,111,187,25,95,59,186,185,274,111,261,72,272,42,137,235,62,86,144,193,77,146,265,156,54,188,40,49,125,110,16,29,218,219,68,138,268,70,223,296,142,146,247,49,133,310,131,63,60,94,315,59,240,177,14,226,332,164,94,53,227,33,130,331,97,23,316,114,271,67,339,330,247,299,189,278,158,283,54,215,49,219,157,31,344,128,37,213,335,57,298,102,9,356,99,362,342,133,14,121,30,64,314,102,318,209,41,34,57,247,77,219,96,248,177,238,169,268,342,347,256,31,278,118,369,33,395,229,16,218,158,208,250,9,335,75,93,146,399,230,116,357,372,282,257,193,152,269,131,233,258,7,376,170,222,244,242,393,407,154,47,286,191,422,340,217,83,209,233,374,355,144,87,266,238,44,363,197,240,377,297,167,453,282,279,387,358,254,107,414,427,117,220,342,333,177,199,396,280,113,22,348,14,424,162,86,339,219,141,408,432,117,108,400,436,236,195,145,456,295,371,122,69,360,312,197,108,326,396,259,161,197,20,385,369,225,161,8,182,358,215,224,167,124,42,225,263,96,100,26,129,330,524,214,247,187,31,380,334,183,251,254,366,336,56,482,491,206,278,39,162,107,14,441,13,189,330,297,238,104,298,552,491,456,480,310,396,73,205,59,177,208,75,447,520,394,402,332,507,157,268,196,388,249,179,498,493,471,577,501,85,316,580,508,502,458,488,241,316,363,395,259,589,113,255,256,364,240,288,27,304,172,182,73,319,126,152,172,379,170,420,110,151,156,199,217,258,560,383,132,379,290,537,76,360,281,329,389,568,425,440,487,553,466,531,318,619,541,23,25,246,27,205,157,226,212,445,193,420,338,249,457,250,439,594,12,285,256,298,68,265,290,287,391,47,443,524,650,193,104,202,344,234,449,639,385,98,519,237,591,228,305,457,441,518,631,73,112,346,74,298,500,539,673,588,670,248,316,262,513,705,405,140,229,260,339,639,477,637,706,125,218,609,196,600,89,285,377,472,508,697,485,24,142,535,421,76,176,320,358,597,641,643,590,320,407,554,518,250,194,459,434,110,660,203,475,530,719,313,686,275,411,735,727,285,146,572,627,160,369,82,398,320,169,421,508,187,123,356,384,747,64,449,101,26,118,228,410,684,540,179,299,726,16,385,44,737,97,391,344,88,740,197,436,713,114,433,308,38,140,377,785,223,65,422,505,192,333,771,645,169,263,679,245,389,396,823,64,458,671,117,57,795,16,477,422,96,75,343,501,418,359,230,552,274,590,77,392,773,650,464,419,783,159,20,584,223,424,843,111,708,590,127,483,793,164,628,510,479,408,633,159,635,708,173,553,125,162,76,841,369,716,324,529,638,852,445,669,31,481,243,814,752,90,632,813,209,546,662,196,810,894,761,700,219,629,892,535,779,714,706,806,272,578,157,233,866,297,786,123,576,793,312,396,57,264,223,829,639,219,508,853,527,560,116,501,866,200,933,292,573,867,575,885,454,607,199,329,69,428,199,229,892,257,611,770,636,787,213,635,420,790,479,134,164,386,145,475,33,882,585,107,428,867,766,669,540,967,559,855,526,696,973,592,184,635,321,262,237,474,60,715,183,35,678,261,941,244,131,192,656,335,609,154,669,947,635,952,589,79,825,891,569,63,685,918,850,64,377,58,526,75,268,754,535,925,696,116,879,999,708,1019,880,984,71,923,810,394,127,450,198,409,835,348,143,524,194,178,54,545,274,840,608,604,14,819,417,787,509,965,322,1013,661,310,867,983,900,194,815,238,1061,262,1063,714,316,613,559,725,239,899,447,87,151,862,902,327,110,612,118,212,123,626,407,816,832,994,705,59,943,529,193,437,1068,660,410,982,377,838,728,1017,738,375,1023,489,81,758,433,774,938,936,734,281,1036,567,1010,477,194,830,309,939,902,984,1059,619,212,591,480,818,483,951,811,129,212,170,307,1020,781,112,958,62,125,402,181,676,726,1149,718,222,1091,506,329,988,634,843,639,436,1133,509,295,921,668,89,1023,376,96,829,471,966,1136,238,1135,283,184,1124,870,997,1024,479,1109,970,841,1009,62,387,264,875,668,118,789,320,46,765,891,692,819,614,295,1004,520,1013,914,473,280,610,775,1148,982,680,478,1017,1141,269,1093,686,550,1000,672,50,133,871,538,82,117,365,466,984,712,127,517,490,482,112,798,634,342,504,778,184,1153,656,567,748,1157,451,546,1168,1224,1252,104,836,566,321,185,322,184,282,2,681,263,836,956,389,63,1062,1195,176,65,797,737,195,360,678,394,1202,843,932,747,906,11,786,586,41,1214,244,209,1132,872,742,785,1209,961,481,183,1187,889,63,1235,1112,680,364,359,1073,1027,530,236,76,82,580,135,1057,776,424,835,960,994,860,574,341,1307,743,730,151,82,298,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46,266,1030,577,1290,980,1001,2819,2914,473,3393,2279,2135,1514,693,590,1766,1445,208,2974,2578,3451,3031,2797,2546,1145,1712,2681,1665,1465,1188,195,2766,402,270,2259,2024,652,2511,2712,2766,1879,1737,3543,417,1518,243,271,2267,2078,3575,2509,3482,2558,1744,804,733,1076,1748,1152,654,1917,3311,1115,285,3085,2865,1993,1219,3464,2937,1320,1411,116,128,1457,1304,3417,3406,2237,1932,667,193,2773,2282,728,2288,2873,2823,1519,1572,3365,2778,1375,1164,366,3313,1682,2001,3530,271,3355,2823,748,874,2642,2512,650,425,3494,101,627,1772,1098,809,2807,2231,83,918,2063,2187,944,1139,3634,3660,2325,2362,1054,1029,2627,1988,805,3672,2932,2631,1065,1386,3184,3319,2137,1881,130,115,2726,2092,1623,1889,3022,2852,1720,1626,433,3559,1669,2475,791,173,3413,3539,1026,2070,196,3208,1957,2030,972,3165,3162,2702,1712,2137,3323,3491,2029,2083,977,433,2638,2154,1249,1302,3495,3505,2234,2162,633,627,3212,332,1635,360,380,3293,2364,2856,3637,411,3168,3488,2739,1945,3311,196,2285,2161,648,1590,2348,3073,2983,1103,1362,540,1307,2544,1011,1300,3756,49,2142,2060,1065,710,3180,333,1415,1255,508,3037,183,769,3586,256,3770,399,2888,2130,3594,454,3394,3290,1733,2823,623,1463,2950,3661,1982,2869,3096,3576,3550,2225,2434,2035,2451,3795,2886,2272,1011,969,3057,3201,1956,1877,1347,1950,2864,2743,2510,2037,971,115,2042,3063,1964,1124,391,748,2690,3084,1932,1789,1105,1057,3140,2322,1543,612,3388,1405,1635,1974,2464,2176,1137,3726,2773,2785,1736,1672,3623,1384,2366,2625,2409,1679,474,840,2641,2560,1136,2281,336,199,1669,2202,1762,1542,386,3777,3226,3015,1762,2110,192,522,3387,2643,2482,2219,295,3845,2276,2874,1892,1441,1234,764,3026,598,3014,3345,1090,2088,3419,3375,1420,1648,1935,2587,3098,374,3779,2570,2196,2164,3532,793,2842,2715,2274,2688,1097,1312,266,3640,2051,3376,1321,981,568,3813,3100,3424,941,2310,493,42,3918,3354,2460,2178,750,1145,3862,710,2646,1839,1614,2081,526,895,2207,2453,1629,1715,1324,1018,2608,391,2843,2785,1936,2082,1239,2925,3268,3195,2478,3126,3031,984,887,3743,49,2579,1304,2396,23,486,2966,73,1701,2257,2142,2199,891,1525,2586,2910,2256,2745,860,880,2521,3649,3471,3135,3084,2671,546,87,3544,2944,2971,575,1254,497,411,1038,3763,3959,1760,2713,498,1205,1339,1644,2578,12,2565,2782,1885,1327,3883,3883,80,8,3006,3551,647,1441,785,847,783,3555,2198,2160,2129,1306,1503,791,2592,3550,3199,3227,2478,2271,1042,3768,3473,3914,2527,37,1166,2612,787,958,1434,1595,2681,2743,2720,1875,691,2034,3763,620,186,3762,3400,2421,1356,1926,208,907,3186,797,2295,3121,2616,2045,1013,2442,72,3794,3316,3594,3046,93,597,1409,691,1350,1015,419,3286,3372,1284,2695,1241,2618,63,4059,694,890,3176,3960,2007,1574,1131,2361,1053,455,2968,260,2705,3252,1734,2375,658,1138,1143,763,3584,68,2511,2870,2289,3144,821,1334,3415,620,3650,3180,3332,3775,1691,2199,1886,787,3845,839,3900,3276,2458,2303,2409,3539,3682,1952,4098,870,728,79,2596,2670,1842,1664,939,2654,20,1246,1087,1154,811,11,2771,1423,1841,1948,2463,1463,3199,647,4074,4020,3674,292,2572,3634,3097,2811,422,2618,3713,3582,76,3203,3993,3272,1769,3043,1527,1571,947,1793,2909,1163,4184,431,3312,4128,2322,2243,1069,1782,1175,3326,2361,939,3918,1193,3507,3662,1494,2574,1085,2075,1818,2938,1054,1155,970,1067,3656,892,2098,2244,2874,1917,2738,3069,713,1514,473,221,723,294,2253,3056,2751,2958,2440,3053,1460,1145,384,1357,1645,383,3860,3743,2912,3216,2235,3720,973,3041,1816,2418,1744,2229,581,3733,4135,999,3392,1921,1724,3551,3161,3118,3401,2998,1247,2306,890,1374,398,2199,3007,119,3842,4228,2784,3435,2949,2875,2117,2254,1693,1870,3784,445,438,4266,229,1513,3454,83,3448,3470,1784,3899,2620,2477,1759,2552,3017,1698,130,982,54,197,413,968,3227,339,3834,206,2824,3149,1923,1848,1411,2344,1446,3215,430,992,1051,920,354,1519,3404,769,4051,3301,2578,62,2792,3354,1989,3405,1569,2228,2170,2149,1306,884,889,2392,3738,1147,791,3867,4046,49,3032,3806,3368,4290,2067,94,1623,2950,1658,1835,2689,1938,629,1445,896,255,624,1508,51,1278,900,254,4071,862,3624,2468,3137,3690,3487,4292,941,2471,3659,2508,2303,2513,1561,1562,871,1010,554,1022,3432,4382,1188,1806,3953,1954,4104,19,2724,3839,3749,93,1861,3775,3650,3640,2611,2906,605,2845,1897,2804,2184,3946,2436,2058,968,1543,1332,1663,4048,1024,26,117,471,1273,3795,696,4172,4320,3314,449,3275,3591,3277,3134,3676,1364,1718,3057,2725,3246,3816,3371,1569,2426,2118,2721,1673,3621,1457,2444,2399,2364,2496,2741,1465,1487,436,1465,2383,2215,3778,785,597,698,327,1233,4260,4270,202,457,577,1181,3505,364,63,245,225,191,3156,434,3760,4299,3674,4011,2606,3711,3319,3609,3283,4462,3687,3806,2693,3064,2826,154,2010,3110,3191,3758,3632,4292,2444,3138,2140,3348,1858,3831,2438,2367,3168,2933,2749,4019,2292,2895,2131,2752,2217,2656,1606,2645,2175,3015,1520,3204,1970,1744,1776,2650,1921,4503,1880,1937,1760,2785,1803,1355,416,1920,1294,1548,1557,2569,973,3083,2432,3112,1502,2971,1050,1319,2197,856,2557,4053,4525,3183,1908,2915,2638,2203,1162,2446,1924,3945,1338,3064,2041,2874,2712,2581,2244,3442,2539,2589,2279,2669,2146,3609,1626,3350,2469,2625,2143,3895,2448,3163,2011,2997,2849,4487,2330,2728,3142,2977,3665,4256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int main()
{
    int t;scanf("%d",&t);
    while(t--)
    {
        int n;scanf("%d",&n);
        cout<<a[n]<<endl;
    }
}