Consider a sequence $A$ of integers, containing $N$ integers between $1$ and $N$. Each integer appears exactly once in the sequence.

A subsequence of $A$ is a sequence obtained by removing some (possibly none) numbers from the beginning of $A$, and then from the end of $A$.

Calculate how many different subsequences of $A$ of odd length have their median equal to $B$. The median of a sequence is the element in the middle of the sequence after it is sorted. For example, the median of the sequence $(5, 1, 3)$ is $3$.

-----Input-----
The first line contains two integers, $N$ ($1 \le N \le 100000$) and $B$ ($1 \le B \le N$).

The second line contains $N$ integers separated by spaces, the elements of sequence $A$.

-----Output-----
Output the number of subsequences of $A$ whose median is $B$.

-----Explanation of Sample Input-----
In Sample Input 3, the four subsequences of $A$ with median $4$ are $(4)$, $(7, 2, 4)$, $(5, 7, 2, 4, 3)$ and $(5, 7, 2, 4, 3, 1, 6)$.

-----Examples-----
Sample Input 1:
5 4
1 2 3 4 5
Sample Output 1:
2

Sample Input 2:
6 3
1 2 4 5 6 3
Sample Output 2:
1

Difficulty: interview

Starter code:

Solutions: