Choose Integers

We ask you to select some number of positive integers, and calculate the sum of them.

It is allowed to select as many integers as you like, and as large integers as you wish. You have to follow these, however: each selected integer needs to be a multiple of A, and you need to select at least one integer.

Your objective is to make the sum congruent to C modulo B. Determine whether this is possible.

If the objective is achievable, print YES. Otherwise, print NO.

Constraints

• 1 ≤ A ≤ 100
• 1 ≤ B ≤ 100
• 0 ≤ C < B

Input

Input is given from Standard Input in the following format:

A B C

Output

Print YES or NO.

Examples

Input

7 5 1

Output

YES

Input

2 2 1

Output

NO

Input

1 100 97

Output

YES

Input

40 98 58

Output

YES

Input

77 42 36

Output

NO

inputFormat

Input

Input is given from Standard Input in the following format:

A B C

outputFormat

Output

Print YES or NO.

Examples

Input

7 5 1

Output

YES

Input

2 2 1

Output

NO

Input

1 100 97

Output

YES

Input

40 98 58

Output

YES

Input

77 42 36

Output

NO

样例

7 5 1

YES