#include <bits/stdc++.h>

using namespace std;

int main() {
  int n, m;
  scanf("%d %d", &n, &m);
  map<int, int> r;
  r[0] = 1;
  long long ans = 0;
  for (int i = 0, s = 0; i < n; i++) {
    int a;
    scanf("%d", &a);
    s = (s + a) % m;
    if (r.count(s)) ans += r[s];
    r[s]++;
  }
  printf("%lld\n", ans);
  cerr << (double) clock() / CLOCKS_PER_SEC << '\n';
  return 0;
}
### Prompt

Please create a solution in Cpp 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 main() {
  int n, m;
  scanf("%d %d", &n, &m);
  map<int, int> r;
  r[0] = 1;
  long long ans = 0;
  for (int i = 0, s = 0; i < n; i++) {
    int a;
    scanf("%d", &a);
    s = (s + a) % m;
    if (r.count(s)) ans += r[s];
    r[s]++;
  }
  printf("%lld\n", ans);
  cerr << (double) clock() / CLOCKS_PER_SEC << '\n';
  return 0;
}
```