Partial Sums ZOJ - 1569

Given a series of n numbers a1, a2, …, an, the partial sum of the numbers is defined as the sum of ai, ai+1, …, aj.

You are supposed to calculate how many partial sums of a given series of numbers could be divided evenly by a given number m.

Input

There are multiple test, each contains 2 lines.

The first line is 2 positive integers n (n <= 10000 ) and m (m <= 5000).

The second line contains n non-negative integers a1, a2, …, an. Numbers are separated by one or several spaces.

The input is ended by EOF.

Output

One test each line - the number of partial sums which could be divided by m.

Sample Input

5 4
1 2 3 4 5
6 7
9 8 7 6 5 4

Sample Output

2
3