Problem2531--Modulo Sum

2531: Modulo Sum

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Time Limit : 2.000 sec  Memory Limit : 256 MiB

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Description

time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

You are given a sequence of numbers a1,a2,...,an, and a number m.

Check if it is possible to choose a non-empty subsequence aij 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≤106, 2≤m≤103) − the size of the original sequence and the number such that sum should be divisible by it.

The second line contains n integers a1,a2,...,an (0≤ai≤109).

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.

Source/Category

 
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