A call center records the number of calls received in each of n consecutive minutes. A "surge window" is any block of exactly k consecutive minutes whose total call count is at least t. Count how many surge windows occur.
Input format
Line 1: three integers n, k, and t.
Line 2: n space-separated non-negative integers, the per-minute call counts.
Output format
A single integer: the number of length-k windows whose sum is at least t.
Constraints
- 1 ≤ k ≤ n ≤ 100000
- 0 ≤ each call count ≤ 1000000
- 0 ≤ t ≤ 1000000000000