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 = list(map(int, input().split()))
c_list.sort()
dp_list = [0] + [10**9]*(n)
for i in range(1, n+1):
    for c in c_list:
        if i - c >= 0:
            dp_list[i] = min(dp_list[i], dp_list[i-c]+1)
        else:
            break
print(dp_list[-1])