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 = [int(i) for i in input().split()]
dp = [[-1 for _ in range(m + 1)] for _ in range(n + 1)]
for i in range(1, n + 1):
    dp[i][1] = i
for j in range(1, m + 1):
    dp[0][j] = 0
    # dp[1][j] = 1
for i in range(n + 1):
    for j in range(1, m):
        if c[j] > i:
            dp[i][j + 1] = dp[i][j]
        else:
            dp[i][j + 1] = min(dp[i][j], dp[i - c[j]][j + 1] + 1)
print(dp[n][m])