Farmer John has lined up his $N$ cows in a row to measure their heights; cow $i$ has height $H_i$ nanometers--FJ believes in precise measurements! He wants to take a picture of some contiguous subsequence of the cows to submit to a bovine photography contest at the county fair.

The fair has a very strange rule about all submitted photos: a photograph is only valid to submit if it depicts a group of cows whose median height is at least a certain threshold $X$.

For purposes of this problem, we define the median of an array $A_{0\ldots K}$ to be $A_{\lceil \frac{K}{2}\rceil}$ after $A$ is sorted, where $\lceil \frac{K}{2}\rceil$ gives $\frac{K}{2}$ rounded up to the nearest integer (or $\frac{K}{2}$ itself, it $\frac{K}{2}$ is an integer to begin with). For example the median of $\{7, 3, 2, 6\}$ is $6$, and the median of $\{5, 4, 8\}$ is $5$.

Please help FJ count the number of different contiguous subsequences of hiscows that he could potentially submit to the photography contest.

• $1 \leqslant N \leqslant 100,000$
• $1 \leqslant H_i \leqslant 1,000,000,000$
• $1 \leqslant X \leqslant 1,000,000,000$

Input Format

• Line $1$: Two space-separated integers: $N$ and $X$.
• Lines $2..N+1$: Line $i+1$ contains the single integer $H_i$.

Output Format:

• Line $1$: The number of subsequences of FJ's cows that have median at least $X$. Note this may not fit into a 32-bit integer.

4 6
10
5
6
2

7

Sample Details

Input Details:

FJ's four cows have heights $10$, $5$, $6$, $2$. We want to know how many contiguous subsequences have median at least $6$.

Output Details:

There are $10$ possible contiguous subsequences to consider. Of these, only $7$ have median at least $6$. They are $\{10\}$, $\{6\}$, $\{10, 5\}$, $\{5, 6\}$, $\{6, 2\}$, $\{10, 5, 6\}$, $\{10, 5, 6, 2\}$.