A factory floor sensor reports one integer temperature reading per minute. You are given the full sequence of n readings, a window length k, and an integer alert threshold t.

Consider every contiguous window of exactly k consecutive readings (there are n - k + 1 such windows, each one starting one minute later than the previous one). A window triggers an alert when the AVERAGE of its k readings is greater than or equal to t. Compare the average exactly, without rounding: a window with sum S triggers an alert exactly when S >= t * k.

Count how many of the n - k + 1 windows trigger an alert.

Input format

Line 1: three integers n, k, t separated by spaces. Line 2: n space-separated integers, the readings in chronological order.

Output format

A single integer: the number of windows whose average is >= t.

Constraints

• 1 <= k <= n <= 100000
• -1000 <= each reading <= 1000
• -1000 <= t <= 1000

4 2 4
3 5 1 6

1

6 3 0
-2 -2 -2 5 5 5

3