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B. Modulo Sum

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given a sequence of numbers *a*_{1}, *a*_{2}, ..., *a*_{n}, and a number *m*.

Check if it is possible to choose a non-empty subsequence *a*_{ij} such that the sum of numbers in this subsequence is divisible by *m*.

Input

The first line contains two numbers, *n* and *m* (1 ≤ *n* ≤ 10^{6}, 2 ≤ *m* ≤ 10^{3}) — the size of the original sequence and the number such that sum should be divisible by it.

The second line contains *n* integers *a*_{1}, *a*_{2}, ..., *a*_{n} (0 ≤ *a*_{i} ≤ 10^{9}).

Output

In the single line print either "YES" (without the quotes) if there exists the sought subsequence, or "NO" (without the quotes), if such subsequence doesn't exist.

Examples

Input

3 5

1 2 3

Output

YES

Input

1 6

5

Output

NO

Input

4 6

3 1 1 3

Output

YES

Input

6 6

5 5 5 5 5 5

Output

YES

Note

In the first sample test you can choose numbers 2 and 3, the sum of which is divisible by 5.

In the second sample test the single non-empty subsequence of numbers is a single number 5. Number 5 is not divisible by 6, that is, the sought subsequence doesn't exist.

In the third sample test you need to choose two numbers 3 on the ends.

In the fourth sample test you can take the whole subsequence.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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