E2. Median on Segments (General Case Edition)time limit per test3 secondsmemory limit per test256 megabytesinputstandard inputoutputstandard 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.InputThe 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).OutputPrint the required number.ExamplesInput5 41 4 5 60 4Output8Input3 11 1 1Output6Input15 21 2 3 1 2 3 1 2 3 1 2 3 1 2 3Output97NoteIn 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).
Input5 41 4 5 60 4
Output8
['sortings', '*2400']