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: Wrong Answer)

def cs(n, p, c):
    global count, m
    if n % c[0] == 0:
        count = min(count, p + n // c[0])
        return count
    elif p + n // c[0] >= count:
        return m
    elif c[0] < n:
        return min(cs(n - c[0], p + 1, c), cs(n, p, c[1:]))
    else:
        return cs(n, p, c[1:])

n, m = map(int, input().split())
c = list(map(int, input().split()))
c.sort(reverse = True)
count = n
print(cs(n, 0, c))