#include <iostream>
#include <map>

using ll = long long;

int main(){
  ll n,m,a[100001]={0}, wa[100001]={0};
  std::cin>>n>>m;
  ll sum=0, ans=0;
  std::map<int, int> p{{0,1}};
  for(int i=0;i<n;++i){
    std::cin>>a[i];
    sum += a[i];
    wa[i+1]=sum;
    p[wa[i+1]%m]++;
  }

  for(auto it: p){
    ll pi = it.second;
    ans += pi* (pi-1)/2;
  }
  std::cout<<ans<<std::endl;
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 <map>

using ll = long long;

int main(){
  ll n,m,a[100001]={0}, wa[100001]={0};
  std::cin>>n>>m;
  ll sum=0, ans=0;
  std::map<int, int> p{{0,1}};
  for(int i=0;i<n;++i){
    std::cin>>a[i];
    sum += a[i];
    wa[i+1]=sum;
    p[wa[i+1]%m]++;
  }

  for(auto it: p){
    ll pi = it.second;
    ans += pi* (pi-1)/2;
  }
  std::cout<<ans<<std::endl;
  return 0;
}

```