You are given a sequence of \(N\) integers \(a_1, a_2, \dots, a_N\) and an integer \(K\). Your task is to count the number of intervals \([l, r] \) such that \(a_l + a_r + min(a_l, a_{l + 1}, \dots, a_r) \le K\).

Input format

First line: Two space-separated integers \(N, K\)
Second line: \(N\) space-separated integers denoting the elements of the sequence

Output format

Print the answer in a single line.

Constraints

\(1 \le N \le 5\times10^5\), \(80\%\) test cases \(N \le 2\times 10^5\)

\(1 \le K \le 10^{18}\)

\(1 \le a_i \le 10^{18}\)