p02851 AtCoder Beginner Contest 146 - Rem of Sum is Num_16989
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
# -*- coding: utf-8 -*-
import sys
from collections import defaultdict

N,K=map(int, sys.stdin.readline().split())
if K==1:
    print 0
    quit()
A=map(int, sys.stdin.readline().split())
A=map(lambda a: (a-1)%K, A)

S=[0]
for a in A:
    S.append( (S[-1]+a)%K )   #累積和

d=dict()    #要素：要素の数を持つ

ans=0
for i in range(N+1):
    x=S[i]%K
    if i==0:
        d[x]=1
    else:
        if x in d:
            ans+=d[x]   #自分より前に同じ出現した、自分と同じ要素の数を答えに追加
            d[x]+=1
        else:
            d[x]=1      
        if 0<=i-K+1:
            x_head=S[i-K+1]%K  #長さK-1の範囲で配列Sを見るため、１つ進んだら一番先頭の要素を辞書から削除する
            d[x_head]-=1

print ans
        