Question
Divisible Shift Windows

You are given an integer array and a positive integer k. Count the number of non-empty contiguous subarrays whose sum is divisible by k.

The answer may be large, so use a 64-bit integer.

Input

The first line contains KaTeX can only parse string typed expression and KaTeX can only parse string typed expression.
The second line contains KaTeX can only parse string typed expression integers.

Output

Print the number of non-empty subarrays whose sum is divisible by KaTeX can only parse string typed expression.

Example
Input:
6 5

4 5 0 -2 -3 1
Output:
7

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