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()))
INF = 10**5
dp = [INF for _ in range(n+1)]
dp[0] = 0
for i in range(n):
    for c in C:
        if i + c <= n:
            dp[i+c] = min(dp[i+c], dp[i]+1)
print(dp[n])