#include <bits/stdc++.h>
#define int long long

using namespace std;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  map<int, int> cnt;
  ++cnt[0];
  int sum = 0, ans = 0;
  for (int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    sum = (sum + a) % m;
    ans += cnt[sum];
    ++cnt[sum];
  } 
  cout << ans << '\n';
  return 0;
}
### Prompt

Your task is to create 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>
#define int long long

using namespace std;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  int n, m;
  cin >> n >> m;
  map<int, int> cnt;
  ++cnt[0];
  int sum = 0, ans = 0;
  for (int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    sum = (sum + a) % m;
    ans += cnt[sum];
    ++cnt[sum];
  } 
  cout << ans << '\n';
  return 0;
}
```