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=[int(i) for i in input().split(" ")]
c=sorted([int(i) for i in input().split(" ")])
c.pop(0)
table=[[0 for j in range(n+1)] for i in range(m)]
for j in range(n+1):
    table[0][j]=j
for i in range(1,m):
    for j in range(n+1):
        if j>=c[i-1]:
            table[i][j]=min(table[i-1][j],table[i-1][j-c[i-1]]+1,table[i][j-c[i-1]]+1)
        else:
            table[i][j]=table[i-1][j]

print(table[-1][-1])