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 = int(input().split()[0])
c = list(filter(lambda x:x <= n,map(int,input().split())))
m = len(c)

minimum = [n] * (n+1)
minimum[0] = 0
for i in c:
    minimum[i] = 1

for i in range(1,n+1):
    for j in range(m):
        if c[j]<=i and minimum[i-c[j]] + 1 < minimum[i]:
            minimum[i] = minimum[i-c[j]]+1

print(minimum[n])