Subset Sum Divisible by K

You are given an integer m representing the number of integers, a positive integer k (the divisor), and a list of m integers. Your task is to determine whether there exists a non-empty contiguous subsequence (subarray) whose sum is divisible by k.

Note: Although the problem statement refers to it as a subset, the intended solution checks for a contiguous segment of numbers. Use the prefix sum modulo technique to efficiently solve the problem.

Example:
For m = 5, k = 3 and the sequence [1, 2, 3, 4, 5], the subarray [1, 2] sums to 3, which is divisible by 3, so the answer is "YES".

inputFormat

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

outputFormat

Output a single line containing YES if there exists a non-empty contiguous subsequence whose sum is divisible by k, or NO otherwise.

5 3
1 2 3 4 5

YES