Problem D
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 |