#include<cstdio>
#include<vector>
#include<map>
using namespace std;
typedef long long ll;
int main()
{
    int a,b;
    scanf("%d%d",&a,&b);
    vector<ll> v(a),s(a+1,0);
    for(int i=0;i<a;i++)
    {
        scanf("%lld",&v[i]);
        v[i]--;
        s[i+1] = (s[i]+v[i]+b)%b;
    }

    map<int,int> mp;
    ll ans=0;
    for(int i=0;i<=a;i++)
    {
        if(i-b>=0)mp[s[i-b]]--;
        ans += mp[s[i]];
        mp[s[i]]++;
    }
    printf("%lld\n",ans);
    return 0;
}
### Prompt

Your task is to create a cpp solution to the following problem:

Given are a sequence of N positive integers A_1, A_2, \ldots, A_N, and a positive integer K.

Find the number of non-empty contiguous subsequences in A such that the remainder when dividing the sum of its elements by K is equal to the number of its elements. We consider two subsequences different if they are taken from different positions, even if they are equal sequences.

Constraints

* All values in input are integers.
* 1 \leq N \leq 2\times 10^5
* 1 \leq K \leq 10^9
* 1 \leq A_i \leq 10^9

Input

Input is given from Standard Input in the following format:


N K
A_1 A_2 \cdots A_N


Output

Print the number of subsequences that satisfy the condition.

Examples

Input

5 4
1 4 2 3 5


Output

4


Input

8 4
4 2 4 2 4 2 4 2


Output

7


Input

10 7
14 15 92 65 35 89 79 32 38 46


Output

8

### Response

```cpp
#include<cstdio>
#include<vector>
#include<map>
using namespace std;
typedef long long ll;
int main()
{
    int a,b;
    scanf("%d%d",&a,&b);
    vector<ll> v(a),s(a+1,0);
    for(int i=0;i<a;i++)
    {
        scanf("%lld",&v[i]);
        v[i]--;
        s[i+1] = (s[i]+v[i]+b)%b;
    }

    map<int,int> mp;
    ll ans=0;
    for(int i=0;i<=a;i++)
    {
        if(i-b>=0)mp[s[i-b]]--;
        ans += mp[s[i]];
        mp[s[i]]++;
    }
    printf("%lld\n",ans);
    return 0;
}
```