Reference: Codeforces 577B — Modulo Sum

You are given a sequence of ~n~ non-negative integers:

~a_1, a_2, \ldots, a_n~

and an integer ~m~.

Determine whether it is possible to choose a non-empty subsequence whose sum is divisible by ~m~.

The chosen elements do not need to be consecutive.

Input

• The first line contains two integers: ~n~ and ~m~.
• The second line contains ~n~ integers: ~a_1, a_2, \ldots, a_n~.

Output

• Print YES if there exists a non-empty subsequence whose sum is divisible by ~m~.
• Otherwise, print NO.

Constraints

• ~1 \le n \le 10^6~
• ~2 \le m \le 10^3~
• ~0 \le a_i \le 10^9~

Example 1

Input:

3 5
1 2 3

Output:

YES