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()))

DP = [[100000 for _ in range(n+1)] for _ in range(m+1)]
DP[0][0] = 0

for i in range(m):
    for j in range(n+1):
        if(j >= c[i]):
            DP[i+1][j] = min(DP[i][j], DP[i+1][j-c[i]]+1)
        else:
            DP[i+1][j] = DP[i][j]

print(DP[m][n])