English · Original
Chinese · Translation
Formal · Original
You 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 $m$.
## Input
The 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 $a_1, a_2, \dots, a_n$ ($1 \le a_i \le 2\cdot10^5$).
## Output
Print the required number.
[samples]
## Note
In the first example, the suitable pairs of indices are: $(1, 3)$, $(1, 4)$, $(1, 5)$, $(2, 2)$, $(2, 3)$, $(2, 5)$, $(4, 5)$ and $(5, 5)$.
你被给定一个整数序列 $a_1, a_2, dots.h, a_n$。
求满足 $1 lt.eq l lt.eq r lt.eq n$ 的下标对 $(l, r)$ 的数量，使得子序列 $a_l, a_(l + 1), dots.h, a_r$ 的中位数恰好等于给定的数 $m$。
一个序列的中位数是指将序列按非降序排序后位于中间位置的元素。如果序列长度为偶数，则使用两个中间元素中靠左的那个。
例如，若 $a = [ 4, 2, 7, 5 ]$，则其中位数为 $4$，因为排序后序列为 $[ 2, 4, 5, 7 ]$，两个中间元素中靠左的是 $4$。序列 $[ 7, 1, 2, 9, 6 ]$ 的中位数为 $6$，因为排序后 $6$ 位于序列正中间。
编写一个程序，求满足子序列 $a_l, a_(l + 1), dots.h, a_r$ 的中位数恰好等于给定数 $m$ 的下标对 $(l, r)$（$1 lt.eq l lt.eq r lt.eq n$）的数量。
第一行包含两个整数 $n$ 和 $m$（$1 lt.eq n, m lt.eq 2 dot.op 10^5$），分别表示给定序列的长度和要求的中位数值。
第二行包含一个整数序列 $a_1, a_2, dots.h, a_n$（$1 lt.eq a_i lt.eq 2 dot.op 10^5$）。
请输出所求的数量。
在第一个例子中，符合条件的下标对为：$(1, 3)$、$(1, 4)$、$(1, 5)$、$(2, 2)$、$(2, 3)$、$(2, 5)$、$(4, 5)$ 和 $(5, 5)$。
## Input
第一行包含两个整数 $n$ 和 $m$（$1 lt.eq n, m lt.eq 2 dot.op 10^5$），分别表示给定序列的长度和要求的中位数值。第二行包含一个整数序列 $a_1, a_2, dots.h, a_n$（$1 lt.eq a_i lt.eq 2 dot.op 10^5$）。
## Output
请输出所求的数量。
[samples]
## Note
在第一个例子中，符合条件的下标对为：$(1, 3)$、$(1, 4)$、$(1, 5)$、$(2, 2)$、$(2, 3)$、$(2, 5)$、$(4, 5)$ 和 $(5, 5)$。
**Definitions**
Let $ n \in \mathbb{Z}^+ $ be the length of the sequence.
Let $ m \in \mathbb{Z}^+ $ be the target median value.
Let $ A = (a_1, a_2, \dots, a_n) $ be a sequence of integers, where $ a_i \in \mathbb{Z}^+ $ for all $ i \in \{1, \dots, n\} $.
For a contiguous subsequence $ A[l:r] = (a_l, a_{l+1}, \dots, a_r) $ with $ 1 \leq l \leq r \leq n $, define its **median** as the element at position $ \left\lfloor \frac{r - l + 2}{2} \right\rfloor $ in the sorted version of $ A[l:r] $.
**Constraints**
1. $ 1 \leq n \leq 2 \cdot 10^5 $
2. $ 1 \leq m \leq 2 \cdot 10^5 $
3. $ 1 \leq a_i \leq 2 \cdot 10^5 $ for all $ i \in \{1, \dots, n\} $
**Objective**
Compute the number of pairs $ (l, r) $ with $ 1 \leq l \leq r \leq n $ such that the median of $ A[l:r] $ is exactly $ m $.
API Response (JSON)
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