#include <bits/stdc++.h>

using namespace std;

int b[111111];
int main() {
	int n, m;
	cin >> n >> m;
	for (int i = 0; i < n; i++) {
		int a;
		scanf("%d", &a);
		b[i + 1] = (b[i] + a) % m;
	}
	sort(b, b + n + 1);
	long r = 0;
	m = 1;
	for (int i = 0; i < n; i++) {
		if (b[i] != b[i + 1])
			m = 0;
		r += m++;
	}
	cout << r << endl;
	return 0;
}

### Prompt

Your challenge is to write a CPP solution to the following problem:

There are N boxes arranged in a row from left to right. The i-th box from the left contains A_i candies.

You will take out the candies from some consecutive boxes and distribute them evenly to M children.

Such being the case, find the number of the pairs (l, r) that satisfy the following:

* l and r are both integers and satisfy 1 \leq l \leq r \leq N.
* A_l + A_{l+1} + ... + A_r is a multiple of M.

Constraints

* All values in input are integers.
* 1 \leq N \leq 10^5
* 2 \leq M \leq 10^9
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N M
A_1 A_2 ... A_N


Output

Print the number of the pairs (l, r) that satisfy the conditions.

Note that the number may not fit into a 32-bit integer type.

Examples

Input

3 2
4 1 5


Output

3


Input

13 17
29 7 5 7 9 51 7 13 8 55 42 9 81


Output

6


Input

10 400000000
1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000 1000000000


Output

25

### Response

```cpp
#include <bits/stdc++.h>

using namespace std;

int b[111111];
int main() {
	int n, m;
	cin >> n >> m;
	for (int i = 0; i < n; i++) {
		int a;
		scanf("%d", &a);
		b[i + 1] = (b[i] + a) % m;
	}
	sort(b, b + n + 1);
	long r = 0;
	m = 1;
	for (int i = 0; i < n; i++) {
		if (b[i] != b[i + 1])
			m = 0;
		r += m++;
	}
	cout << r << endl;
	return 0;
}

```