Stable Transaction Periods

Given an array of non-negative integers, find the length of the longest non-empty contiguous subarray whose sum is divisible by k; output 0 if there is none.

This site's standard input/output is stated explicitly.

输入格式

The first line contains n k, and the second line contains n integers. 1≤n≤100000, 0≤a[i]≤10⁹, 1≤k≤10⁹.

输出格式

Output one integer answer.

样例 1

输入：

6 3
2 7 6 1 4 5

输出：

4

样例 2

输入：

1 2
1

输出：

0

样例 3

输入：

2 7
0 0

输出：

2

样例说明

Example 1: 7, 6, 1, 4 sum to 18, giving length 4; there is no longer valid range. Example 2: the only element 1 is not divisible by 2, so the output is 0. Example 3: the whole range sums to 0, which is divisible by 7, so the output is 2.