Picking Peaches

Problem Description

There are $n$ people picking peaches in an orchard. The $n$ people stand in a line, and from left to right the number of peaches each person has is $a_i$.

The orchard has a free-peach rule: if the total number of peaches held by $x$ consecutive people, divided by $k$, leaves a remainder exactly equal to $x$, then those $x$ people can get peaches for free. Moreover, there is only one chance per day to get peaches for free.

Figure out how many different ways there are for someone to get peaches for free today.

Input Format

The first line contains two integers $n$ and $k$.

The next line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output Format

One integer: the answer.

Sample Input

8 4
4 2 4 2 4 2 4 2

Sample Output

7

Sample Explanation

The seven different schemes are: $a_1, a_2$; $a_2, a_3$; $a_3, a_4$; $a_4, a_5$; $a_5, a_6$; $a_6, a_7$; $a_7, a_8$.

Note: two schemes are different as long as at least one boundary of the contiguous segment differs.

Constraints

For all data, $1 \le n \le 2 \times 10^5$, $1 \le k \le 10^9$, $1 \le a_i \le 10^9$.