Contiguous Subsequence Divisibility

Given an integer sequence $a_1, a_2, \ldots, a_n$ and an integer $k$, determine whether there exists a contiguous subsequence (i.e. a subarray) whose sum is divisible by $k$. Formally, find if there exist indices $i$ and $j$ with $1 \le i \le j \le n$ such that $$\sum_{t=i}^{j}a_t \equiv 0 \pmod{k}.$$

The input will contain the length of the sequence, the modulus $k$, and the $n$ integers in the sequence. If such a subsequence exists, output YES; otherwise, output NO.

inputFormat

The input is given via standard input (stdin).

The first line contains two integers $n$ and $k$, where $n$ is the number of integers in the sequence and $k$ is the divisor.
The second line contains $n$ space-separated integers representing the sequence.

outputFormat

Output a single line to standard output (stdout):

If there exists a contiguous subsequence whose sum is divisible by $k$, print YES. Otherwise, print NO.## sample

5 3
1 2 3 4 5

YES