Rem of Sum is Num

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

inputFormat

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

outputFormat

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

样例

5 4
1 4 2 3 5

4