Codeforces #319 B-modulo Sum (drawer principle, DP)

B-modulo SumTime limit:2000MS Memory Limit:262144KB 64bit IO Format:%i64d &%i6 4u SubmitStatus

Description

You are given a sequence of numbers a_{1, a2, ..., an, and a Number m.}

Check if it is possible to choose a non-empty subsequence a_{iJ such that sum of Numbers in this subsequence are divisible by M.}

Input

The first line contains 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 is divisible by it.}

The second line contains n integers a_{1, a2, ..., an ( C10>0≤ ai ≤10^9).}

Output

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

Sample Input

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

Hint

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

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

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

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

The backpack is still not well understood.

Because every time it is in that one-dimensional form.

The practice of this problem is similar to the 01 backpack.

In addition there can be an optimization ...

When the n>m ... The principle of eradicating drawers. Must be yes.

The complexity can be from O (nm) excellent to O (m^2)

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Codeforces #319 B-modulo Sum (drawer principle, DP)