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E2. Median on Segments (General Case Edition)

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given an integer sequence $$$a_1, a_2, \dots, a_n$$$.

Find the number of pairs of indices $$$(l, r)$$$ ($$$1 \le l \le r \le n$$$) such that the value of median of $$$a_l, a_{l+1}, \dots, a_r$$$ is exactly the given number $$$m$$$.

The median of a sequence is the value of an element which is in the middle of the sequence after sorting it in non-decreasing order. If the length of the sequence is even, the left of two middle elements is used.

For example, if $$$a=[4, 2, 7, 5]$$$ then its median is $$$4$$$ since after sorting the sequence, it will look like $$$[2, 4, 5, 7]$$$ and the left of two middle elements is equal to $$$4$$$. The median of $$$[7, 1, 2, 9, 6]$$$ equals $$$6$$$ since after sorting, the value $$$6$$$ will be in the middle of the sequence.

Write a program to find the number of pairs of indices $$$(l, r)$$$ ($$$1 \le l \le r \le n$$$) such that the value of median of $$$a_l, a_{l+1}, \dots, a_r$$$ is exactly the given number $$$m$$$.

Input

The first line contains integers $$$n$$$ and $$$m$$$ ($$$1 \le n,m \le 2\cdot10^5$$$) — the length of the given sequence and the required value of the median.

The second line contains an integer sequence $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 2\cdot10^5$$$).

Output

Print the required number.

Examples

Input

5 4

1 4 5 60 4

Output

8

Input

3 1

1 1 1

Output

6

Input

15 2

1 2 3 1 2 3 1 2 3 1 2 3 1 2 3

Output

97

Note

In the first example, the suitable pairs of indices are: $$$(1, 3)$$$, $$$(1, 4)$$$, $$$(1, 5)$$$, $$$(2, 2)$$$, $$$(2, 3)$$$, $$$(2, 5)$$$, $$$(4, 5)$$$ and $$$(5, 5)$$$.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

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