You are given an array ~a~ of length ~N~. You want to count the number of subarrays of length ~K~ whose sum is strictly larger than the sum of any subarray of length ~K-1~.

Input Specification

The first line will contain the integers ~N, K~ ~(2 \le K \le N \le 10^5)~.

The second line will contain ~N~ integers, ~a_i~ ~(|a_i| \le 10^4)~.

Output Specification

Output the number of subarrays of length ~K~ whose sum is strictly larger than the sum of any subarray of length ~K-1~.

Subtasks

Subtask 1 [30%]

~N \le 10^3~

Subtask 2 [70%]

No further constraints.

Sample Input

4 2
2 3 2 4

Sample Output

3