Coin Changing Problem

Find the minimum number of coins to make change for n cents using coins of denominations d₁, d₂,.., d_m. 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

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