Average Voodoo Doll Price

Mirko has been buying voodoo dolls. He wants to buy as cheaply as possible, so he writes down the price of a doll every day. His price list holds the doll prices of the last $N$ days, and the price $a_i$ is the price of a doll $i$ days ago.

Mirko thinks the average price over a run of consecutive days is connected to the price on the next day. While testing that hunch he ran into another question. For a given $P$, how many runs of consecutive days within the last $N$ days had an average doll price greater than or equal to $P$?

Two runs of consecutive days count as different when they start at different positions or end at different positions.

The first line contains the sequence length $N$. ($1 \le N \le 1\,000\,000$)

The second line contains the $N$ prices $a_i$. ($0 \le a_i \le 1\,000\,000\,000$)

The third line contains an integer $P$. ($0 \le P \le 1\,000\,000\,000$)

Print on the first line the number of consecutive runs whose average price is greater than or equal to $P$.

In the first example the only run whose average is at least 3 is {3}.

In the second example the runs whose average is at least 2 are {1, 3}, {1, 3, 2}, {3}, {3, 2}, {2}.