C. Ginger's sequence
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Ginger gives you a sequence of length $$$n$$$, please ask if there are two non-empty different subsequences in this sequence, such that $$$s_1 \equiv s_2 \pmod k$$$, $$$s_1, s_2$$$ are the sum of the two subsequences respectively.

If there exist, output $$$\text{YES}$$$, otherwise output $$$\text{NO}$$$.

Input

The first line contains two integers $$$n, k$$$ $$$(1 \le n,k \le 10 ^ 5)$$$ indicating the lenth of sequence and modulo.

The second line contains $$$n$$$ integers $$$a_1,a_2, \dots, a_n$$$ indicating the sequence.

Output

Print $$$\text{YES}$$$ or $$$\text{NO}$$$.

Example
Input
5 10
1 2 3 4 5
Output
YES
Note

Subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements.