Problem: There are n students living in the campus. Every morning all students wake up at the same time and go to wash. There are m rooms with wash basins. The i-th of these rooms contains ai wash basins. Every student independently select one the rooms with equal probability and goes to it. After all students selected their rooms, students in each room divide into queues by the number of wash basins so that the size of the largest queue is the least possible. Calculate the expected value of the size of the largest queue among all rooms.

Input

The first line contains two positive integers n and m (1 ≤ n, m ≤ 50) — the amount of students and the amount of rooms. The second line contains m integers a1, a2, ... , am (1 ≤ ai ≤ 50). ai means the amount of wash basins in the i-th room.

Output

Output single number: the expected value of the size of the largest queue. Your answer must have an absolute or relative error less than 10 - 9.

Examples

Input

1 1
2


Output

1.00000000000000000000


Input

2 2
1 1


Output

1.50000000000000000000


Input

2 3
1 1 1


Output

1.33333333333333350000


Input

7 5
1 1 2 3 1


Output

2.50216960000000070000

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int maxn = 123;
int a[maxn], n, m;
double pw[maxn], C[maxn][maxn], dp[maxn][maxn][maxn];
void init() {
  pw[0] = 1;
  for (int i = 1; i <= n; i++) pw[i] = pw[i - 1] / m;
  C[0][0] = 1.0;
  C[1][0] = 1.0;
  C[1][1] = 1.0;
  C[2][0] = 1.0;
  C[2][1] = 2.0;
  C[2][2] = 1.0;
  C[3][0] = 1.0;
  C[3][1] = 3.0;
  C[3][2] = 3.0;
  C[3][3] = 1.0;
  C[4][0] = 1.0;
  C[4][1] = 4.0;
  C[4][2] = 6.0;
  C[4][3] = 4.0;
  C[4][4] = 1.0;
  C[5][0] = 1.0;
  C[5][1] = 5.0;
  C[5][2] = 10.0;
  C[5][3] = 10.0;
  C[5][4] = 5.0;
  C[5][5] = 1.0;
  C[6][0] = 1.0;
  C[6][1] = 6.0;
  C[6][2] = 15.0;
  C[6][3] = 20.0;
  C[6][4] = 15.0;
  C[6][5] = 6.0;
  C[6][6] = 1.0;
  C[7][0] = 1.0;
  C[7][1] = 7.0;
  C[7][2] = 21.0;
  C[7][3] = 35.0;
  C[7][4] = 35.0;
  C[7][5] = 21.0;
  C[7][6] = 7.0;
  C[7][7] = 1.0;
  C[8][0] = 1.0;
  C[8][1] = 8.0;
  C[8][2] = 28.0;
  C[8][3] = 56.0;
  C[8][4] = 70.0;
  C[8][5] = 56.0;
  C[8][6] = 28.0;
  C[8][7] = 8.0;
  C[8][8] = 1.0;
  C[9][0] = 1.0;
  C[9][1] = 9.0;
  C[9][2] = 36.0;
  C[9][3] = 84.0;
  C[9][4] = 126.0;
  C[9][5] = 126.0;
  C[9][6] = 84.0;
  C[9][7] = 36.0;
  C[9][8] = 9.0;
  C[9][9] = 1.0;
  C[10][0] = 1.0;
  C[10][1] = 10.0;
  C[10][2] = 45.0;
  C[10][3] = 120.0;
  C[10][4] = 210.0;
  C[10][5] = 252.0;
  C[10][6] = 210.0;
  C[10][7] = 120.0;
  C[10][8] = 45.0;
  C[10][9] = 10.0;
  C[10][10] = 1.0;
  C[11][0] = 1.0;
  C[11][1] = 11.0;
  C[11][2] = 55.0;
  C[11][3] = 165.0;
  C[11][4] = 330.0;
  C[11][5] = 462.0;
  C[11][6] = 462.0;
  C[11][7] = 330.0;
  C[11][8] = 165.0;
  C[11][9] = 55.0;
  C[11][10] = 11.0;
  C[11][11] = 1.0;
  C[12][0] = 1.0;
  C[12][1] = 12.0;
  C[12][2] = 66.0;
  C[12][3] = 220.0;
  C[12][4] = 495.0;
  C[12][5] = 792.0;
  C[12][6] = 924.0;
  C[12][7] = 792.0;
  C[12][8] = 495.0;
  C[12][9] = 220.0;
  C[12][10] = 66.0;
  C[12][11] = 12.0;
  C[12][12] = 1.0;
  C[13][0] = 1.0;
  C[13][1] = 13.0;
  C[13][2] = 78.0;
  C[13][3] = 286.0;
  C[13][4] = 715.0;
  C[13][5] = 1287.0;
  C[13][6] = 1716.0;
  C[13][7] = 1716.0;
  C[13][8] = 1287.0;
  C[13][9] = 715.0;
  C[13][10] = 286.0;
  C[13][11] = 78.0;
  C[13][12] = 13.0;
  C[13][13] = 1.0;
  C[14][0] = 1.0;
  C[14][1] = 14.0;
  C[14][2] = 91.0;
  C[14][3] = 364.0;
  C[14][4] = 1001.0;
  C[14][5] = 2002.0;
  C[14][6] = 3003.0;
  C[14][7] = 3432.0;
  C[14][8] = 3003.0;
  C[14][9] = 2002.0;
  C[14][10] = 1001.0;
  C[14][11] = 364.0;
  C[14][12] = 91.0;
  C[14][13] = 14.0;
  C[14][14] = 1.0;
  C[15][0] = 1.0;
  C[15][1] = 15.0;
  C[15][2] = 105.0;
  C[15][3] = 455.0;
  C[15][4] = 1365.0;
  C[15][5] = 3003.0;
  C[15][6] = 5005.0;
  C[15][7] = 6435.0;
  C[15][8] = 6435.0;
  C[15][9] = 5005.0;
  C[15][10] = 3003.0;
  C[15][11] = 1365.0;
  C[15][12] = 455.0;
  C[15][13] = 105.0;
  C[15][14] = 15.0;
  C[15][15] = 1.0;
  C[16][0] = 1.0;
  C[16][1] = 16.0;
  C[16][2] = 120.0;
  C[16][3] = 560.0;
  C[16][4] = 1820.0;
  C[16][5] = 4368.0;
  C[16][6] = 8008.0;
  C[16][7] = 11440.0;
  C[16][8] = 12870.0;
  C[16][9] = 11440.0;
  C[16][10] = 8008.0;
  C[16][11] = 4368.0;
  C[16][12] = 1820.0;
  C[16][13] = 560.0;
  C[16][14] = 120.0;
  C[16][15] = 16.0;
  C[16][16] = 1.0;
  C[17][0] = 1.0;
  C[17][1] = 17.0;
  C[17][2] = 136.0;
  C[17][3] = 680.0;
  C[17][4] = 2380.0;
  C[17][5] = 6188.0;
  C[17][6] = 12376.0;
  C[17][7] = 19448.0;
  C[17][8] = 24310.0;
  C[17][9] = 24310.0;
  C[17][10] = 19448.0;
  C[17][11] = 12376.0;
  C[17][12] = 6188.0;
  C[17][13] = 2380.0;
  C[17][14] = 680.0;
  C[17][15] = 136.0;
  C[17][16] = 17.0;
  C[17][17] = 1.0;
  C[18][0] = 1.0;
  C[18][1] = 18.0;
  C[18][2] = 153.0;
  C[18][3] = 816.0;
  C[18][4] = 3060.0;
  C[18][5] = 8568.0;
  C[18][6] = 18564.0;
  C[18][7] = 31824.0;
  C[18][8] = 43758.0;
  C[18][9] = 48620.0;
  C[18][10] = 43758.0;
  C[18][11] = 31824.0;
  C[18][12] = 18564.0;
  C[18][13] = 8568.0;
  C[18][14] = 3060.0;
  C[18][15] = 816.0;
  C[18][16] = 153.0;
  C[18][17] = 18.0;
  C[18][18] = 1.0;
  C[19][0] = 1.0;
  C[19][1] = 19.0;
  C[19][2] = 171.0;
  C[19][3] = 969.0;
  C[19][4] = 3876.0;
  C[19][5] = 11628.0;
  C[19][6] = 27132.0;
  C[19][7] = 50388.0;
  C[19][8] = 75582.0;
  C[19][9] = 92378.0;
  C[19][10] = 92378.0;
  C[19][11] = 75582.0;
  C[19][12] = 50388.0;
  C[19][13] = 27132.0;
  C[19][14] = 11628.0;
  C[19][15] = 3876.0;
  C[19][16] = 969.0;
  C[19][17] = 171.0;
  C[19][18] = 19.0;
  C[19][19] = 1.0;
  C[20][0] = 1.0;
  C[20][1] = 20.0;
  C[20][2] = 190.0;
  C[20][3] = 1140.0;
  C[20][4] = 4845.0;
  C[20][5] = 15504.0;
  C[20][6] = 38760.0;
  C[20][7] = 77520.0;
  C[20][8] = 125970.0;
  C[20][9] = 167960.0;
  C[20][10] = 184756.0;
  C[20][11] = 167960.0;
  C[20][12] = 125970.0;
  C[20][13] = 77520.0;
  C[20][14] = 38760.0;
  C[20][15] = 15504.0;
  C[20][16] = 4845.0;
  C[20][17] = 1140.0;
  C[20][18] = 190.0;
  C[20][19] = 20.0;
  C[20][20] = 1.0;
  C[21][0] = 1.0;
  C[21][1] = 21.0;
  C[21][2] = 210.0;
  C[21][3] = 1330.0;
  C[21][4] = 5985.0;
  C[21][5] = 20349.0;
  C[21][6] = 54264.0;
  C[21][7] = 116280.0;
  C[21][8] = 203490.0;
  C[21][9] = 293930.0;
  C[21][10] = 352716.0;
  C[21][11] = 352716.0;
  C[21][12] = 293930.0;
  C[21][13] = 203490.0;
  C[21][14] = 116280.0;
  C[21][15] = 54264.0;
  C[21][16] = 20349.0;
  C[21][17] = 5985.0;
  C[21][18] = 1330.0;
  C[21][19] = 210.0;
  C[21][20] = 21.0;
  C[21][21] = 1.0;
  C[22][0] = 1.0;
  C[22][1] = 22.0;
  C[22][2] = 231.0;
  C[22][3] = 1540.0;
  C[22][4] = 7315.0;
  C[22][5] = 26334.0;
  C[22][6] = 74613.0;
  C[22][7] = 170544.0;
  C[22][8] = 319770.0;
  C[22][9] = 497420.0;
  C[22][10] = 646646.0;
  C[22][11] = 705432.0;
  C[22][12] = 646646.0;
  C[22][13] = 497420.0;
  C[22][14] = 319770.0;
  C[22][15] = 170544.0;
  C[22][16] = 74613.0;
  C[22][17] = 26334.0;
  C[22][18] = 7315.0;
  C[22][19] = 1540.0;
  C[22][20] = 231.0;
  C[22][21] = 22.0;
  C[22][22] = 1.0;
  C[23][0] = 1.0;
  C[23][1] = 23.0;
  C[23][2] = 253.0;
  C[23][3] = 1771.0;
  C[23][4] = 8855.0;
  C[23][5] = 33649.0;
  C[23][6] = 100947.0;
  C[23][7] = 245157.0;
  C[23][8] = 490314.0;
  C[23][9] = 817190.0;
  C[23][10] = 1144066.0;
  C[23][11] = 1352078.0;
  C[23][12] = 1352078.0;
  C[23][13] = 1144066.0;
  C[23][14] = 817190.0;
  C[23][15] = 490314.0;
  C[23][16] = 245157.0;
  C[23][17] = 100947.0;
  C[23][18] = 33649.0;
  C[23][19] = 8855.0;
  C[23][20] = 1771.0;
  C[23][21] = 253.0;
  C[23][22] = 23.0;
  C[23][23] = 1.0;
  C[24][0] = 1.0;
  C[24][1] = 24.0;
  C[24][2] = 276.0;
  C[24][3] = 2024.0;
  C[24][4] = 10626.0;
  C[24][5] = 42504.0;
  C[24][6] = 134596.0;
  C[24][7] = 346104.0;
  C[24][8] = 735471.0;
  C[24][9] = 1307504.0;
  C[24][10] = 1961256.0;
  C[24][11] = 2496144.0;
  C[24][12] = 2704156.0;
  C[24][13] = 2496144.0;
  C[24][14] = 1961256.0;
  C[24][15] = 1307504.0;
  C[24][16] = 735471.0;
  C[24][17] = 346104.0;
  C[24][18] = 134596.0;
  C[24][19] = 42504.0;
  C[24][20] = 10626.0;
  C[24][21] = 2024.0;
  C[24][22] = 276.0;
  C[24][23] = 24.0;
  C[24][24] = 1.0;
  C[25][0] = 1.0;
  C[25][1] = 25.0;
  C[25][2] = 300.0;
  C[25][3] = 2300.0;
  C[25][4] = 12650.0;
  C[25][5] = 53130.0;
  C[25][6] = 177100.0;
  C[25][7] = 480700.0;
  C[25][8] = 1081575.0;
  C[25][9] = 2042975.0;
  C[25][10] = 3268760.0;
  C[25][11] = 4457400.0;
  C[25][12] = 5200300.0;
  C[25][13] = 5200300.0;
  C[25][14] = 4457400.0;
  C[25][15] = 3268760.0;
  C[25][16] = 2042975.0;
  C[25][17] = 1081575.0;
  C[25][18] = 480700.0;
  C[25][19] = 177100.0;
  C[25][20] = 53130.0;
  C[25][21] = 12650.0;
  C[25][22] = 2300.0;
  C[25][23] = 300.0;
  C[25][24] = 25.0;
  C[25][25] = 1.0;
  C[26][0] = 1.0;
  C[26][1] = 26.0;
  C[26][2] = 325.0;
  C[26][3] = 2600.0;
  C[26][4] = 14950.0;
  C[26][5] = 65780.0;
  C[26][6] = 230230.0;
  C[26][7] = 657800.0;
  C[26][8] = 1562275.0;
  C[26][9] = 3124550.0;
  C[26][10] = 5311735.0;
  C[26][11] = 7726160.0;
  C[26][12] = 9657700.0;
  C[26][13] = 10400600.0;
  C[26][14] = 9657700.0;
  C[26][15] = 7726160.0;
  C[26][16] = 5311735.0;
  C[26][17] = 3124550.0;
  C[26][18] = 1562275.0;
  C[26][19] = 657800.0;
  C[26][20] = 230230.0;
  C[26][21] = 65780.0;
  C[26][22] = 14950.0;
  C[26][23] = 2600.0;
  C[26][24] = 325.0;
  C[26][25] = 26.0;
  C[26][26] = 1.0;
  C[27][0] = 1.0;
  C[27][1] = 27.0;
  C[27][2] = 351.0;
  C[27][3] = 2925.0;
  C[27][4] = 17550.0;
  C[27][5] = 80730.0;
  C[27][6] = 296010.0;
  C[27][7] = 888030.0;
  C[27][8] = 2220075.0;
  C[27][9] = 4686825.0;
  C[27][10] = 8436285.0;
  C[27][11] = 13037895.0;
  C[27][12] = 17383860.0;
  C[27][13] = 20058300.0;
  C[27][14] = 20058300.0;
  C[27][15] = 17383860.0;
  C[27][16] = 13037895.0;
  C[27][17] = 8436285.0;
  C[27][18] = 4686825.0;
  C[27][19] = 2220075.0;
  C[27][20] = 888030.0;
  C[27][21] = 296010.0;
  C[27][22] = 80730.0;
  C[27][23] = 17550.0;
  C[27][24] = 2925.0;
  C[27][25] = 351.0;
  C[27][26] = 27.0;
  C[27][27] = 1.0;
  C[28][0] = 1.0;
  C[28][1] = 28.0;
  C[28][2] = 378.0;
  C[28][3] = 3276.0;
  C[28][4] = 20475.0;
  C[28][5] = 98280.0;
  C[28][6] = 376740.0;
  C[28][7] = 1184040.0;
  C[28][8] = 3108105.0;
  C[28][9] = 6906900.0;
  C[28][10] = 13123110.0;
  C[28][11] = 21474180.0;
  C[28][12] = 30421755.0;
  C[28][13] = 37442160.0;
  C[28][14] = 40116600.0;
  C[28][15] = 37442160.0;
  C[28][16] = 30421755.0;
  C[28][17] = 21474180.0;
  C[28][18] = 13123110.0;
  C[28][19] = 6906900.0;
  C[28][20] = 3108105.0;
  C[28][21] = 1184040.0;
  C[28][22] = 376740.0;
  C[28][23] = 98280.0;
  C[28][24] = 20475.0;
  C[28][25] = 3276.0;
  C[28][26] = 378.0;
  C[28][27] = 28.0;
  C[28][28] = 1.0;
  C[29][0] = 1.0;
  C[29][1] = 29.0;
  C[29][2] = 406.0;
  C[29][3] = 3654.0;
  C[29][4] = 23751.0;
  C[29][5] = 118755.0;
  C[29][6] = 475020.0;
  C[29][7] = 1560780.0;
  C[29][8] = 4292145.0;
  C[29][9] = 10015005.0;
  C[29][10] = 20030010.0;
  C[29][11] = 34597290.0;
  C[29][12] = 51895935.0;
  C[29][13] = 67863915.0;
  C[29][14] = 77558760.0;
  C[29][15] = 77558760.0;
  C[29][16] = 67863915.0;
  C[29][17] = 51895935.0;
  C[29][18] = 34597290.0;
  C[29][19] = 20030010.0;
  C[29][20] = 10015005.0;
  C[29][21] = 4292145.0;
  C[29][22] = 1560780.0;
  C[29][23] = 475020.0;
  C[29][24] = 118755.0;
  C[29][25] = 23751.0;
  C[29][26] = 3654.0;
  C[29][27] = 406.0;
  C[29][28] = 29.0;
  C[29][29] = 1.0;
  C[30][0] = 1.0;
  C[30][1] = 30.0;
  C[30][2] = 435.0;
  C[30][3] = 4060.0;
  C[30][4] = 27405.0;
  C[30][5] = 142506.0;
  C[30][6] = 593775.0;
  C[30][7] = 2035800.0;
  C[30][8] = 5852925.0;
  C[30][9] = 14307150.0;
  C[30][10] = 30045015.0;
  C[30][11] = 54627300.0;
  C[30][12] = 86493225.0;
  C[30][13] = 119759850.0;
  C[30][14] = 145422675.0;
  C[30][15] = 155117520.0;
  C[30][16] = 145422675.0;
  C[30][17] = 119759850.0;
  C[30][18] = 86493225.0;
  C[30][19] = 54627300.0;
  C[30][20] = 30045015.0;
  C[30][21] = 14307150.0;
  C[30][22] = 5852925.0;
  C[30][23] = 2035800.0;
  C[30][24] = 593775.0;
  C[30][25] = 142506.0;
  C[30][26] = 27405.0;
  C[30][27] = 4060.0;
  C[30][28] = 435.0;
  C[30][29] = 30.0;
  C[30][30] = 1.0;
  C[31][0] = 1.0;
  C[31][1] = 31.0;
  C[31][2] = 465.0;
  C[31][3] = 4495.0;
  C[31][4] = 31465.0;
  C[31][5] = 169911.0;
  C[31][6] = 736281.0;
  C[31][7] = 2629575.0;
  C[31][8] = 7888725.0;
  C[31][9] = 20160075.0;
  C[31][10] = 44352165.0;
  C[31][11] = 84672315.0;
  C[31][12] = 141120525.0;
  C[31][13] = 206253075.0;
  C[31][14] = 265182525.0;
  C[31][15] = 300540195.0;
  C[31][16] = 300540195.0;
  C[31][17] = 265182525.0;
  C[31][18] = 206253075.0;
  C[31][19] = 141120525.0;
  C[31][20] = 84672315.0;
  C[31][21] = 44352165.0;
  C[31][22] = 20160075.0;
  C[31][23] = 7888725.0;
  C[31][24] = 2629575.0;
  C[31][25] = 736281.0;
  C[31][26] = 169911.0;
  C[31][27] = 31465.0;
  C[31][28] = 4495.0;
  C[31][29] = 465.0;
  C[31][30] = 31.0;
  C[31][31] = 1.0;
  C[32][0] = 1.0;
  C[32][1] = 32.0;
  C[32][2] = 496.0;
  C[32][3] = 4960.0;
  C[32][4] = 35960.0;
  C[32][5] = 201376.0;
  C[32][6] = 906192.0;
  C[32][7] = 3365856.0;
  C[32][8] = 10518300.0;
  C[32][9] = 28048800.0;
  C[32][10] = 64512240.0;
  C[32][11] = 129024480.0;
  C[32][12] = 225792840.0;
  C[32][13] = 347373600.0;
  C[32][14] = 471435600.0;
  C[32][15] = 565722720.0;
  C[32][16] = 601080390.0;
  C[32][17] = 565722720.0;
  C[32][18] = 471435600.0;
  C[32][19] = 347373600.0;
  C[32][20] = 225792840.0;
  C[32][21] = 129024480.0;
  C[32][22] = 64512240.0;
  C[32][23] = 28048800.0;
  C[32][24] = 10518300.0;
  C[32][25] = 3365856.0;
  C[32][26] = 906192.0;
  C[32][27] = 201376.0;
  C[32][28] = 35960.0;
  C[32][29] = 4960.0;
  C[32][30] = 496.0;
  C[32][31] = 32.0;
  C[32][32] = 1.0;
  C[33][0] = 1.0;
  C[33][1] = 33.0;
  C[33][2] = 528.0;
  C[33][3] = 5456.0;
  C[33][4] = 40920.0;
  C[33][5] = 237336.0;
  C[33][6] = 1107568.0;
  C[33][7] = 4272048.0;
  C[33][8] = 13884156.0;
  C[33][9] = 38567100.0;
  C[33][10] = 92561040.0;
  C[33][11] = 193536720.0;
  C[33][12] = 354817320.0;
  C[33][13] = 573166440.0;
  C[33][14] = 818809200.0;
  C[33][15] = 1037158320.0;
  C[33][16] = 1166803110.0;
  C[33][17] = 1166803110.0;
  C[33][18] = 1037158320.0;
  C[33][19] = 818809200.0;
  C[33][20] = 573166440.0;
  C[33][21] = 354817320.0;
  C[33][22] = 193536720.0;
  C[33][23] = 92561040.0;
  C[33][24] = 38567100.0;
  C[33][25] = 13884156.0;
  C[33][26] = 4272048.0;
  C[33][27] = 1107568.0;
  C[33][28] = 237336.0;
  C[33][29] = 40920.0;
  C[33][30] = 5456.0;
  C[33][31] = 528.0;
  C[33][32] = 33.0;
  C[33][33] = 1.0;
  C[34][0] = 1.0;
  C[34][1] = 34.0;
  C[34][2] = 561.0;
  C[34][3] = 5984.0;
  C[34][4] = 46376.0;
  C[34][5] = 278256.0;
  C[34][6] = 1344904.0;
  C[34][7] = 5379616.0;
  C[34][8] = 18156204.0;
  C[34][9] = 52451256.0;
  C[34][10] = 131128140.0;
  C[34][11] = 286097760.0;
  C[34][12] = 548354040.0;
  C[34][13] = 927983760.0;
  C[34][14] = 1391975640.0;
  C[34][15] = 1855967520.0;
  C[34][16] = 2203961430.0;
  C[34][17] = 2333606220.0;
  C[34][18] = 2203961430.0;
  C[34][19] = 1855967520.0;
  C[34][20] = 1391975640.0;
  C[34][21] = 927983760.0;
  C[34][22] = 548354040.0;
  C[34][23] = 286097760.0;
  C[34][24] = 131128140.0;
  C[34][25] = 52451256.0;
  C[34][26] = 18156204.0;
  C[34][27] = 5379616.0;
  C[34][28] = 1344904.0;
  C[34][29] = 278256.0;
  C[34][30] = 46376.0;
  C[34][31] = 5984.0;
  C[34][32] = 561.0;
  C[34][33] = 34.0;
  C[34][34] = 1.0;
  C[35][0] = 1.0;
  C[35][1] = 35.0;
  C[35][2] = 595.0;
  C[35][3] = 6545.0;
  C[35][4] = 52360.0;
  C[35][5] = 324632.0;
  C[35][6] = 1623160.0;
  C[35][7] = 6724520.0;
  C[35][8] = 23535820.0;
  C[35][9] = 70607460.0;
  C[35][10] = 183579396.0;
  C[35][11] = 417225900.0;
  C[35][12] = 834451800.0;
  C[35][13] = 1476337800.0;
  C[35][14] = 2319959400.0;
  C[35][15] = 3247943160.0;
  C[35][16] = 4059928950.0;
  C[35][17] = 4537567650.0;
  C[35][18] = 4537567650.0;
  C[35][19] = 4059928950.0;
  C[35][20] = 3247943160.0;
  C[35][21] = 2319959400.0;
  C[35][22] = 1476337800.0;
  C[35][23] = 834451800.0;
  C[35][24] = 417225900.0;
  C[35][25] = 183579396.0;
  C[35][26] = 70607460.0;
  C[35][27] = 23535820.0;
  C[35][28] = 6724520.0;
  C[35][29] = 1623160.0;
  C[35][30] = 324632.0;
  C[35][31] = 52360.0;
  C[35][32] = 6545.0;
  C[35][33] = 595.0;
  C[35][34] = 35.0;
  C[35][35] = 1.0;
  C[36][0] = 1.0;
  C[36][1] = 36.0;
  C[36][2] = 630.0;
  C[36][3] = 7140.0;
  C[36][4] = 58905.0;
  C[36][5] = 376992.0;
  C[36][6] = 1947792.0;
  C[36][7] = 8347680.0;
  C[36][8] = 30260340.0;
  C[36][9] = 94143280.0;
  C[36][10] = 254186856.0;
  C[36][11] = 600805296.0;
  C[36][12] = 1251677700.0;
  C[36][13] = 2310789600.0;
  C[36][14] = 3796297200.0;
  C[36][15] = 5567902560.0;
  C[36][16] = 7307872110.0;
  C[36][17] = 8597496600.0;
  C[36][18] = 9075135300.0;
  C[36][19] = 8597496600.0;
  C[36][20] = 7307872110.0;
  C[36][21] = 5567902560.0;
  C[36][22] = 3796297200.0;
  C[36][23] = 2310789600.0;
  C[36][24] = 1251677700.0;
  C[36][25] = 600805296.0;
  C[36][26] = 254186856.0;
  C[36][27] = 94143280.0;
  C[36][28] = 30260340.0;
  C[36][29] = 8347680.0;
  C[36][30] = 1947792.0;
  C[36][31] = 376992.0;
  C[36][32] = 58905.0;
  C[36][33] = 7140.0;
  C[36][34] = 630.0;
  C[36][35] = 36.0;
  C[36][36] = 1.0;
  C[37][0] = 1.0;
  C[37][1] = 37.0;
  C[37][2] = 666.0;
  C[37][3] = 7770.0;
  C[37][4] = 66045.0;
  C[37][5] = 435897.0;
  C[37][6] = 2324784.0;
  C[37][7] = 10295472.0;
  C[37][8] = 38608020.0;
  C[37][9] = 124403620.0;
  C[37][10] = 348330136.0;
  C[37][11] = 854992152.0;
  C[37][12] = 1852482996.0;
  C[37][13] = 3562467300.0;
  C[37][14] = 6107086800.0;
  C[37][15] = 9364199760.0;
  C[37][16] = 12875774670.0;
  C[37][17] = 15905368710.0;
  C[37][18] = 17672631900.0;
  C[37][19] = 17672631900.0;
  C[37][20] = 15905368710.0;
  C[37][21] = 12875774670.0;
  C[37][22] = 9364199760.0;
  C[37][23] = 6107086800.0;
  C[37][24] = 3562467300.0;
  C[37][25] = 1852482996.0;
  C[37][26] = 854992152.0;
  C[37][27] = 348330136.0;
  C[37][28] = 124403620.0;
  C[37][29] = 38608020.0;
  C[37][30] = 10295472.0;
  C[37][31] = 2324784.0;
  C[37][32] = 435897.0;
  C[37][33] = 66045.0;
  C[37][34] = 7770.0;
  C[37][35] = 666.0;
  C[37][36] = 37.0;
  C[37][37] = 1.0;
  C[38][0] = 1.0;
  C[38][1] = 38.0;
  C[38][2] = 703.0;
  C[38][3] = 8436.0;
  C[38][4] = 73815.0;
  C[38][5] = 501942.0;
  C[38][6] = 2760681.0;
  C[38][7] = 12620256.0;
  C[38][8] = 48903492.0;
  C[38][9] = 163011640.0;
  C[38][10] = 472733756.0;
  C[38][11] = 1203322288.0;
  C[38][12] = 2707475148.0;
  C[38][13] = 5414950296.0;
  C[38][14] = 9669554100.0;
  C[38][15] = 15471286560.0;
  C[38][16] = 22239974430.0;
  C[38][17] = 28781143380.0;
  C[38][18] = 33578000610.0;
  C[38][19] = 35345263800.0;
  C[38][20] = 33578000610.0;
  C[38][21] = 28781143380.0;
  C[38][22] = 22239974430.0;
  C[38][23] = 15471286560.0;
  C[38][24] = 9669554100.0;
  C[38][25] = 5414950296.0;
  C[38][26] = 2707475148.0;
  C[38][27] = 1203322288.0;
  C[38][28] = 472733756.0;
  C[38][29] = 163011640.0;
  C[38][30] = 48903492.0;
  C[38][31] = 12620256.0;
  C[38][32] = 2760681.0;
  C[38][33] = 501942.0;
  C[38][34] = 73815.0;
  C[38][35] = 8436.0;
  C[38][36] = 703.0;
  C[38][37] = 38.0;
  C[38][38] = 1.0;
  C[39][0] = 1.0;
  C[39][1] = 39.0;
  C[39][2] = 741.0;
  C[39][3] = 9139.0;
  C[39][4] = 82251.0;
  C[39][5] = 575757.0;
  C[39][6] = 3262623.0;
  C[39][7] = 15380937.0;
  C[39][8] = 61523748.0;
  C[39][9] = 211915132.0;
  C[39][10] = 635745396.0;
  C[39][11] = 1676056044.0;
  C[39][12] = 3910797436.0;
  C[39][13] = 8122425444.0;
  C[39][14] = 15084504396.0;
  C[39][15] = 25140840660.0;
  C[39][16] = 37711260990.0;
  C[39][17] = 51021117810.0;
  C[39][18] = 62359143990.0;
  C[39][19] = 68923264410.0;
  C[39][20] = 68923264410.0;
  C[39][21] = 62359143990.0;
  C[39][22] = 51021117810.0;
  C[39][23] = 37711260990.0;
  C[39][24] = 25140840660.0;
  C[39][25] = 15084504396.0;
  C[39][26] = 8122425444.0;
  C[39][27] = 3910797436.0;
  C[39][28] = 1676056044.0;
  C[39][29] = 635745396.0;
  C[39][30] = 211915132.0;
  C[39][31] = 61523748.0;
  C[39][32] = 15380937.0;
  C[39][33] = 3262623.0;
  C[39][34] = 575757.0;
  C[39][35] = 82251.0;
  C[39][36] = 9139.0;
  C[39][37] = 741.0;
  C[39][38] = 39.0;
  C[39][39] = 1.0;
  C[40][0] = 1.0;
  C[40][1] = 40.0;
  C[40][2] = 780.0;
  C[40][3] = 9880.0;
  C[40][4] = 91390.0;
  C[40][5] = 658008.0;
  C[40][6] = 3838380.0;
  C[40][7] = 18643560.0;
  C[40][8] = 76904685.0;
  C[40][9] = 273438880.0;
  C[40][10] = 847660528.0;
  C[40][11] = 2311801440.0;
  C[40][12] = 5586853480.0;
  C[40][13] = 12033222880.0;
  C[40][14] = 23206929840.0;
  C[40][15] = 40225345056.0;
  C[40][16] = 62852101650.0;
  C[40][17] = 88732378800.0;
  C[40][18] = 113380261800.0;
  C[40][19] = 131282408400.0;
  C[40][20] = 137846528820.0;
  C[40][21] = 131282408400.0;
  C[40][22] = 113380261800.0;
  C[40][23] = 88732378800.0;
  C[40][24] = 62852101650.0;
  C[40][25] = 40225345056.0;
  C[40][26] = 23206929840.0;
  C[40][27] = 12033222880.0;
  C[40][28] = 5586853480.0;
  C[40][29] = 2311801440.0;
  C[40][30] = 847660528.0;
  C[40][31] = 273438880.0;
  C[40][32] = 76904685.0;
  C[40][33] = 18643560.0;
  C[40][34] = 3838380.0;
  C[40][35] = 658008.0;
  C[40][36] = 91390.0;
  C[40][37] = 9880.0;
  C[40][38] = 780.0;
  C[40][39] = 40.0;
  C[40][40] = 1.0;
  C[41][0] = 1.0;
  C[41][1] = 41.0;
  C[41][2] = 820.0;
  C[41][3] = 10660.0;
  C[41][4] = 101270.0;
  C[41][5] = 749398.0;
  C[41][6] = 4496388.0;
  C[41][7] = 22481940.0;
  C[41][8] = 95548245.0;
  C[41][9] = 350343565.0;
  C[41][10] = 1121099408.0;
  C[41][11] = 3159461968.0;
  C[41][12] = 7898654920.0;
  C[41][13] = 17620076360.0;
  C[41][14] = 35240152720.0;
  C[41][15] = 63432274896.0;
  C[41][16] = 103077446706.0;
  C[41][17] = 151584480450.0;
  C[41][18] = 202112640600.0;
  C[41][19] = 244662670200.0;
  C[41][20] = 269128937220.0;
  C[41][21] = 269128937220.0;
  C[41][22] = 244662670200.0;
  C[41][23] = 202112640600.0;
  C[41][24] = 151584480450.0;
  C[41][25] = 103077446706.0;
  C[41][26] = 63432274896.0;
  C[41][27] = 35240152720.0;
  C[41][28] = 17620076360.0;
  C[41][29] = 7898654920.0;
  C[41][30] = 3159461968.0;
  C[41][31] = 1121099408.0;
  C[41][32] = 350343565.0;
  C[41][33] = 95548245.0;
  C[41][34] = 22481940.0;
  C[41][35] = 4496388.0;
  C[41][36] = 749398.0;
  C[41][37] = 101270.0;
  C[41][38] = 10660.0;
  C[41][39] = 820.0;
  C[41][40] = 41.0;
  C[41][41] = 1.0;
  C[42][0] = 1.0;
  C[42][1] = 42.0;
  C[42][2] = 861.0;
  C[42][3] = 11480.0;
  C[42][4] = 111930.0;
  C[42][5] = 850668.0;
  C[42][6] = 5245786.0;
  C[42][7] = 26978328.0;
  C[42][8] = 118030185.0;
  C[42][9] = 445891810.0;
  C[42][10] = 1471442973.0;
  C[42][11] = 4280561376.0;
  C[42][12] = 11058116888.0;
  C[42][13] = 25518731280.0;
  C[42][14] = 52860229080.0;
  C[42][15] = 98672427616.0;
  C[42][16] = 166509721602.0;
  C[42][17] = 254661927156.0;
  C[42][18] = 353697121050.0;
  C[42][19] = 446775310800.0;
  C[42][20] = 513791607420.0;
  C[42][21] = 538257874440.0;
  C[42][22] = 513791607420.0;
  C[42][23] = 446775310800.0;
  C[42][24] = 353697121050.0;
  C[42][25] = 254661927156.0;
  C[42][26] = 166509721602.0;
  C[42][27] = 98672427616.0;
  C[42][28] = 52860229080.0;
  C[42][29] = 25518731280.0;
  C[42][30] = 11058116888.0;
  C[42][31] = 4280561376.0;
  C[42][32] = 1471442973.0;
  C[42][33] = 445891810.0;
  C[42][34] = 118030185.0;
  C[42][35] = 26978328.0;
  C[42][36] = 5245786.0;
  C[42][37] = 850668.0;
  C[42][38] = 111930.0;
  C[42][39] = 11480.0;
  C[42][40] = 861.0;
  C[42][41] = 42.0;
  C[42][42] = 1.0;
  C[43][0] = 1.0;
  C[43][1] = 43.0;
  C[43][2] = 903.0;
  C[43][3] = 12341.0;
  C[43][4] = 123410.0;
  C[43][5] = 962598.0;
  C[43][6] = 6096454.0;
  C[43][7] = 32224114.0;
  C[43][8] = 145008513.0;
  C[43][9] = 563921995.0;
  C[43][10] = 1917334783.0;
  C[43][11] = 5752004349.0;
  C[43][12] = 15338678264.0;
  C[43][13] = 36576848168.0;
  C[43][14] = 78378960360.0;
  C[43][15] = 151532656696.0;
  C[43][16] = 265182149218.0;
  C[43][17] = 421171648758.0;
  C[43][18] = 608359048206.0;
  C[43][19] = 800472431850.0;
  C[43][20] = 960566918220.0;
  C[43][21] = 1052049481860.0;
  C[43][22] = 1052049481860.0;
  C[43][23] = 960566918220.0;
  C[43][24] = 800472431850.0;
  C[43][25] = 608359048206.0;
  C[43][26] = 421171648758.0;
  C[43][27] = 265182149218.0;
  C[43][28] = 151532656696.0;
  C[43][29] = 78378960360.0;
  C[43][30] = 36576848168.0;
  C[43][31] = 15338678264.0;
  C[43][32] = 5752004349.0;
  C[43][33] = 1917334783.0;
  C[43][34] = 563921995.0;
  C[43][35] = 145008513.0;
  C[43][36] = 32224114.0;
  C[43][37] = 6096454.0;
  C[43][38] = 962598.0;
  C[43][39] = 123410.0;
  C[43][40] = 12341.0;
  C[43][41] = 903.0;
  C[43][42] = 43.0;
  C[43][43] = 1.0;
  C[44][0] = 1.0;
  C[44][1] = 44.0;
  C[44][2] = 946.0;
  C[44][3] = 13244.0;
  C[44][4] = 135751.0;
  C[44][5] = 1086008.0;
  C[44][6] = 7059052.0;
  C[44][7] = 38320568.0;
  C[44][8] = 177232627.0;
  C[44][9] = 708930508.0;
  C[44][10] = 2481256778.0;
  C[44][11] = 7669339132.0;
  C[44][12] = 21090682613.0;
  C[44][13] = 51915526432.0;
  C[44][14] = 114955808528.0;
  C[44][15] = 229911617056.0;
  C[44][16] = 416714805914.0;
  C[44][17] = 686353797976.0;
  C[44][18] = 1029530696964.0;
  C[44][19] = 1408831480056.0;
  C[44][20] = 1761039350070.0;
  C[44][21] = 2012616400080.0;
  C[44][22] = 2104098963720.0;
  C[44][23] = 2012616400080.0;
  C[44][24] = 1761039350070.0;
  C[44][25] = 1408831480056.0;
  C[44][26] = 1029530696964.0;
  C[44][27] = 686353797976.0;
  C[44][28] = 416714805914.0;
  C[44][29] = 229911617056.0;
  C[44][30] = 114955808528.0;
  C[44][31] = 51915526432.0;
  C[44][32] = 21090682613.0;
  C[44][33] = 7669339132.0;
  C[44][34] = 2481256778.0;
  C[44][35] = 708930508.0;
  C[44][36] = 177232627.0;
  C[44][37] = 38320568.0;
  C[44][38] = 7059052.0;
  C[44][39] = 1086008.0;
  C[44][40] = 135751.0;
  C[44][41] = 13244.0;
  C[44][42] = 946.0;
  C[44][43] = 44.0;
  C[44][44] = 1.0;
  C[45][0] = 1.0;
  C[45][1] = 45.0;
  C[45][2] = 990.0;
  C[45][3] = 14190.0;
  C[45][4] = 148995.0;
  C[45][5] = 1221759.0;
  C[45][6] = 8145060.0;
  C[45][7] = 45379620.0;
  C[45][8] = 215553195.0;
  C[45][9] = 886163135.0;
  C[45][10] = 3190187286.0;
  C[45][11] = 10150595910.0;
  C[45][12] = 28760021745.0;
  C[45][13] = 73006209045.0;
  C[45][14] = 166871334960.0;
  C[45][15] = 344867425584.0;
  C[45][16] = 646626422970.0;
  C[45][17] = 1103068603890.0;
  C[45][18] = 1715884494940.0;
  C[45][19] = 2438362177020.0;
  C[45][20] = 3169870830126.0;
  C[45][21] = 3773655750150.0;
  C[45][22] = 4116715363800.0;
  C[45][23] = 4116715363800.0;
  C[45][24] = 3773655750150.0;
  C[45][25] = 3169870830126.0;
  C[45][26] = 2438362177020.0;
  C[45][27] = 1715884494940.0;
  C[45][28] = 1103068603890.0;
  C[45][29] = 646626422970.0;
  C[45][30] = 344867425584.0;
  C[45][31] = 166871334960.0;
  C[45][32] = 73006209045.0;
  C[45][33] = 28760021745.0;
  C[45][34] = 10150595910.0;
  C[45][35] = 3190187286.0;
  C[45][36] = 886163135.0;
  C[45][37] = 215553195.0;
  C[45][38] = 45379620.0;
  C[45][39] = 8145060.0;
  C[45][40] = 1221759.0;
  C[45][41] = 148995.0;
  C[45][42] = 14190.0;
  C[45][43] = 990.0;
  C[45][44] = 45.0;
  C[45][45] = 1.0;
  C[46][0] = 1.0;
  C[46][1] = 46.0;
  C[46][2] = 1035.0;
  C[46][3] = 15180.0;
  C[46][4] = 163185.0;
  C[46][5] = 1370754.0;
  C[46][6] = 9366819.0;
  C[46][7] = 53524680.0;
  C[46][8] = 260932815.0;
  C[46][9] = 1101716330.0;
  C[46][10] = 4076350421.0;
  C[46][11] = 13340783196.0;
  C[46][12] = 38910617655.0;
  C[46][13] = 101766230790.0;
  C[46][14] = 239877544005.0;
  C[46][15] = 511738760544.0;
  C[46][16] = 991493848554.0;
  C[46][17] = 1749695026860.0;
  C[46][18] = 2818953098830.0;
  C[46][19] = 4154246671960.0;
  C[46][20] = 5608233007146.0;
  C[46][21] = 6943526580276.0;
  C[46][22] = 7890371113950.0;
  C[46][23] = 8233430727600.0;
  C[46][24] = 7890371113950.0;
  C[46][25] = 6943526580276.0;
  C[46][26] = 5608233007146.0;
  C[46][27] = 4154246671960.0;
  C[46][28] = 2818953098830.0;
  C[46][29] = 1749695026860.0;
  C[46][30] = 991493848554.0;
  C[46][31] = 511738760544.0;
  C[46][32] = 239877544005.0;
  C[46][33] = 101766230790.0;
  C[46][34] = 38910617655.0;
  C[46][35] = 13340783196.0;
  C[46][36] = 4076350421.0;
  C[46][37] = 1101716330.0;
  C[46][38] = 260932815.0;
  C[46][39] = 53524680.0;
  C[46][40] = 9366819.0;
  C[46][41] = 1370754.0;
  C[46][42] = 163185.0;
  C[46][43] = 15180.0;
  C[46][44] = 1035.0;
  C[46][45] = 46.0;
  C[46][46] = 1.0;
  C[47][0] = 1.0;
  C[47][1] = 47.0;
  C[47][2] = 1081.0;
  C[47][3] = 16215.0;
  C[47][4] = 178365.0;
  C[47][5] = 1533939.0;
  C[47][6] = 10737573.0;
  C[47][7] = 62891499.0;
  C[47][8] = 314457495.0;
  C[47][9] = 1362649145.0;
  C[47][10] = 5178066751.0;
  C[47][11] = 17417133617.0;
  C[47][12] = 52251400851.0;
  C[47][13] = 140676848445.0;
  C[47][14] = 341643774795.0;
  C[47][15] = 751616304549.0;
  C[47][16] = 1503232609098.0;
  C[47][17] = 2741188875414.0;
  C[47][18] = 4568648125690.0;
  C[47][19] = 6973199770790.0;
  C[47][20] = 9762479679106.0;
  C[47][21] = 12551759587422.0;
  C[47][22] = 14833897694226.0;
  C[47][23] = 16123801841550.0;
  C[47][24] = 16123801841550.0;
  C[47][25] = 14833897694226.0;
  C[47][26] = 12551759587422.0;
  C[47][27] = 9762479679106.0;
  C[47][28] = 6973199770790.0;
  C[47][29] = 4568648125690.0;
  C[47][30] = 2741188875414.0;
  C[47][31] = 1503232609098.0;
  C[47][32] = 751616304549.0;
  C[47][33] = 341643774795.0;
  C[47][34] = 140676848445.0;
  C[47][35] = 52251400851.0;
  C[47][36] = 17417133617.0;
  C[47][37] = 5178066751.0;
  C[47][38] = 1362649145.0;
  C[47][39] = 314457495.0;
  C[47][40] = 62891499.0;
  C[47][41] = 10737573.0;
  C[47][42] = 1533939.0;
  C[47][43] = 178365.0;
  C[47][44] = 16215.0;
  C[47][45] = 1081.0;
  C[47][46] = 47.0;
  C[47][47] = 1.0;
  C[48][0] = 1.0;
  C[48][1] = 48.0;
  C[48][2] = 1128.0;
  C[48][3] = 17296.0;
  C[48][4] = 194580.0;
  C[48][5] = 1712304.0;
  C[48][6] = 12271512.0;
  C[48][7] = 73629072.0;
  C[48][8] = 377348994.0;
  C[48][9] = 1677106640.0;
  C[48][10] = 6540715896.0;
  C[48][11] = 22595200368.0;
  C[48][12] = 69668534468.0;
  C[48][13] = 192928249296.0;
  C[48][14] = 482320623240.0;
  C[48][15] = 1093260079344.0;
  C[48][16] = 2254848913647.0;
  C[48][17] = 4244421484512.0;
  C[48][18] = 7309837001104.0;
  C[48][19] = 11541847896480.0;
  C[48][20] = 16735679449896.0;
  C[48][21] = 22314239266528.0;
  C[48][22] = 27385657281648.0;
  C[48][23] = 30957699535776.0;
  C[48][24] = 32247603683100.0;
  C[48][25] = 30957699535776.0;
  C[48][26] = 27385657281648.0;
  C[48][27] = 22314239266528.0;
  C[48][28] = 16735679449896.0;
  C[48][29] = 11541847896480.0;
  C[48][30] = 7309837001104.0;
  C[48][31] = 4244421484512.0;
  C[48][32] = 2254848913647.0;
  C[48][33] = 1093260079344.0;
  C[48][34] = 482320623240.0;
  C[48][35] = 192928249296.0;
  C[48][36] = 69668534468.0;
  C[48][37] = 22595200368.0;
  C[48][38] = 6540715896.0;
  C[48][39] = 1677106640.0;
  C[48][40] = 377348994.0;
  C[48][41] = 73629072.0;
  C[48][42] = 12271512.0;
  C[48][43] = 1712304.0;
  C[48][44] = 194580.0;
  C[48][45] = 17296.0;
  C[48][46] = 1128.0;
  C[48][47] = 48.0;
  C[48][48] = 1.0;
  C[49][0] = 1.0;
  C[49][1] = 49.0;
  C[49][2] = 1176.0;
  C[49][3] = 18424.0;
  C[49][4] = 211876.0;
  C[49][5] = 1906884.0;
  C[49][6] = 13983816.0;
  C[49][7] = 85900584.0;
  C[49][8] = 450978066.0;
  C[49][9] = 2054455634.0;
  C[49][10] = 8217822536.0;
  C[49][11] = 29135916264.0;
  C[49][12] = 92263734836.0;
  C[49][13] = 262596783764.0;
  C[49][14] = 675248872536.0;
  C[49][15] = 1575580702584.0;
  C[49][16] = 3348108992991.0;
  C[49][17] = 6499270398159.0;
  C[49][18] = 11554258485616.0;
  C[49][19] = 18851684897584.0;
  C[49][20] = 28277527346376.0;
  C[49][21] = 39049918716424.0;
  C[49][22] = 49699896548176.0;
  C[49][23] = 58343356817424.0;
  C[49][24] = 63205303218876.0;
  C[49][25] = 63205303218876.0;
  C[49][26] = 58343356817424.0;
  C[49][27] = 49699896548176.0;
  C[49][28] = 39049918716424.0;
  C[49][29] = 28277527346376.0;
  C[49][30] = 18851684897584.0;
  C[49][31] = 11554258485616.0;
  C[49][32] = 6499270398159.0;
  C[49][33] = 3348108992991.0;
  C[49][34] = 1575580702584.0;
  C[49][35] = 675248872536.0;
  C[49][36] = 262596783764.0;
  C[49][37] = 92263734836.0;
  C[49][38] = 29135916264.0;
  C[49][39] = 8217822536.0;
  C[49][40] = 2054455634.0;
  C[49][41] = 450978066.0;
  C[49][42] = 85900584.0;
  C[49][43] = 13983816.0;
  C[49][44] = 1906884.0;
  C[49][45] = 211876.0;
  C[49][46] = 18424.0;
  C[49][47] = 1176.0;
  C[49][48] = 49.0;
  C[49][49] = 1.0;
  C[50][0] = 1.0;
  C[50][1] = 50.0;
  C[50][2] = 1225.0;
  C[50][3] = 19600.0;
  C[50][4] = 230300.0;
  C[50][5] = 2118760.0;
  C[50][6] = 15890700.0;
  C[50][7] = 99884400.0;
  C[50][8] = 536878650.0;
  C[50][9] = 2505433700.0;
  C[50][10] = 10272278170.0;
  C[50][11] = 37353738800.0;
  C[50][12] = 121399651100.0;
  C[50][13] = 354860518600.0;
  C[50][14] = 937845656300.0;
  C[50][15] = 2250829575120.0;
  C[50][16] = 4923689695575.0;
  C[50][17] = 9847379391150.0;
  C[50][18] = 18053528883775.0;
  C[50][19] = 30405943383200.0;
  C[50][20] = 47129212243960.0;
  C[50][21] = 67327446062800.0;
  C[50][22] = 88749815264600.0;
  C[50][23] = 108043253365600.0;
  C[50][24] = 121548660036300.0;
  C[50][25] = 126410606437752.0;
  C[50][26] = 121548660036300.0;
  C[50][27] = 108043253365600.0;
  C[50][28] = 88749815264600.0;
  C[50][29] = 67327446062800.0;
  C[50][30] = 47129212243960.0;
  C[50][31] = 30405943383200.0;
  C[50][32] = 18053528883775.0;
  C[50][33] = 9847379391150.0;
  C[50][34] = 4923689695575.0;
  C[50][35] = 2250829575120.0;
  C[50][36] = 937845656300.0;
  C[50][37] = 354860518600.0;
  C[50][38] = 121399651100.0;
  C[50][39] = 37353738800.0;
  C[50][40] = 10272278170.0;
  C[50][41] = 2505433700.0;
  C[50][42] = 536878650.0;
  C[50][43] = 99884400.0;
  C[50][44] = 15890700.0;
  C[50][45] = 2118760.0;
  C[50][46] = 230300.0;
  C[50][47] = 19600.0;
  C[50][48] = 1225.0;
  C[50][49] = 50.0;
  C[50][50] = 1.0;
  dp[0][0][0] = 1;
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) scanf("%d", &a[i]);
  init();
  for (int i = 0; i < m; i++) {
    for (int j = 0; j <= n; j++) {
      for (int k = 0; k <= n; k++) {
        if (dp[i][j][k] > 0) {
          for (int l = 0; l <= n - j; l++) {
            int p = l / a[i + 1];
            if (l % a[i + 1]) p++;
            p = max(p, k);
            dp[i + 1][j + l][p] += dp[i][j][k] * C[n - j][l] * pw[l];
          }
        }
      }
    }
  }
  double ans = 0;
  for (int i = 0; i <= n; i++) ans += dp[m][n][i] * i;
  printf("%.15lf\n", ans);
  return 0;
}