#include <bits/stdc++.h>
#define ll long long int
#define MOD 1000000007
#define INF 1000000000000000000

using namespace std;

int main(void){
  ll n, m;
  cin >> n >> m;
  
  ll ans = 0;
  ll sum = 0;
  map<ll,ll> s;
  s[0]++;
  for (int i = 0; i < n; i++){
    ll a;
    cin >> a;
    
    sum = (sum + a) % m;

    ans += s[sum];
    s[sum]++;
  }

  cout << ans << 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>
#define ll long long int
#define MOD 1000000007
#define INF 1000000000000000000

using namespace std;

int main(void){
  ll n, m;
  cin >> n >> m;
  
  ll ans = 0;
  ll sum = 0;
  map<ll,ll> s;
  s[0]++;
  for (int i = 0; i < n; i++){
    ll a;
    cin >> a;
    
    sum = (sum + a) % m;

    ans += s[sum];
    s[sum]++;
  }

  cout << ans << endl;

  return 0;
}

```