#include <iostream>
#include <algorithm>
#include <map>

using namespace std;

int main() {
    int n;
    long m;
    cin >> n >> m;
    map<long, long> mods;
    long rui = 0, sum = 0;
    mods[0] = 1;
    for (int i=0; i<n; i++) {
        long a;
        cin >> a;
        rui = (rui+a) % m;
        sum += mods[rui];
        mods[rui]++;
    }
    cout << sum << '\n';
    return 0;
}
### Prompt

Develop a solution in cpp to the problem described below:

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 <iostream>
#include <algorithm>
#include <map>

using namespace std;

int main() {
    int n;
    long m;
    cin >> n >> m;
    map<long, long> mods;
    long rui = 0, sum = 0;
    mods[0] = 1;
    for (int i=0; i<n; i++) {
        long a;
        cin >> a;
        rui = (rui+a) % m;
        sum += mods[rui];
        mods[rui]++;
    }
    cout << sum << '\n';
    return 0;
}
```