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)




N,M = map(int, input().split())
C = list(map(int, input().split()))

C.sort()
dp = [[float("inf") for _ in range(N+1)] for _ in range(M+1)]
dp[0][0] = 0


#i番目までのコインを使えるときに、j円を作る場合の、コインの最小枚数を求める
for i in range(M):
    for j in range(N+1):
        # i番目を使えない場合
        if C[i] > j:
            dp[i+1][j] = dp[i][j]
        else:
            dp[i+1][j] = min(dp[i][j], dp[i+1][j - C[i]] + 1)

print(dp[-1][-1])