Problem Statement

You are given a sequence of positive integers of length $N$, $A=a_1,a_2,…,a_{N}$, and an integer $K$. How many contiguous subsequences of $A$ satisfy the following condition?

• (Condition) The sum of the elements in the contiguous subsequence is at least $K$.

We consider two contiguous subsequences different if they derive from different positions in $A$, even if they are the same in content.

Note that the answer may not fit into a $32$-bit integer type.

Constraints

• $1 \leq a_i \leq 10^5$
• $1 \leq N \leq 10^5$
• $1 \leq K \leq 10^{10}$

Input

Input is given from Standard Input in the following format:

N K
a_1 a_2 ... a_N

Output

Print the number of contiguous subsequences of $A$ that satisfy the condition.