Problem:
Coin Changing Problem

Find the minimum number of coins to make change for n cents using coins of denominations d1, d2,.., dm. The coins can be used any number of times.

Input

n m
d1 d2 ... dm

Two integers n and m are given in the first line. The available denominations are given in the second line.

Output

Print the minimum number of coins in a line.

Constraints

1 ≤ n ≤ 50000

1 ≤ m ≤ 20

1 ≤ denomination ≤ 10000

The denominations are all different and contain 1.

Sample Input 1

55 4
1 5 10 50

Sample Output 1

2

Sample Input 2

15 6
1 2 7 8 12 50

Sample Output 2

2

Sample Input 3

65 6
1 2 7 8 12 50

Sample Output 3

3

Solution in Python3 (judge verdict: Accepted)

def main():
    n, m = map(int, input().split())
    c = [int(i) for i in input().split()]
    dp = [[10 ** 5 for i in range(n + 1)] for j in range(m + 1)]
    for i in range(m+1):
        dp[i][0] = 0
    for i in range(1, m+1):
        for j in range(1, n+1):
            if c[i - 1] <= j:
                dp[i][j] = min(dp[i][j - c[i - 1]] + 1, dp[i - 1][j])
            else:
                dp[i][j] = dp[i - 1][j]
    print(dp[-1][-1])


if __name__ == '__main__':
    main()