LogiQuest

422. Subarray Sums Divisible by K

MediumPrefix SumModulo

Count the non-empty contiguous subarrays whose sum is divisible by k.

Input format

Line 1: n k Line 2: n integers

Output format

The count.

Example 1

Input

6 5
4 5 0 -2 -3 1

Output

7

Example 2

Input

1 9
5

Output

0

Constraints

1 ≤ n ≤ 10⁵ 2 ≤ k ≤ 10⁴

Read input from standard input and print the answer to standard output. Your code is judged against 5 test cases, most of them hidden.

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