Combinatorial - Coin Changing Problem

Time Limit : 1 sec, Memory Limit : 65536 KB
Japanese version is here

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