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 $N \le 2\times 10^5$

$1 \le K \le 10^{18}$

$1 \le a_i \le 10^{18}$