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2019-01-21 13:00 UTC

Kattis Set 02

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2019-01-28 09:29 UTC
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Problem J
Srednji

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, $N$ ($1 \le N \le 100\, 000$) 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 $(5, 7, 2, 4, 3, 1, 6)$.

Sample Input 1 Sample Output 1
5 4
1 2 3 4 5
2
Sample Input 2 Sample Output 2
6 3
1 2 4 5 6 3
1
Sample Input 3 Sample Output 3
7 4
5 7 2 4 3 1 6
4