Score : $400$ points

问题描述

给定一个长度为 $N$ 的序列 $A=(A_1,A_2,\ldots,A_N)$，以及一个整数 $K$。

请问在序列 $A$ 中有多少个连续子序列的和为 $K$？

换句话说，有多少对整数 $(l,r)$ 满足以下所有条件？

• $1\leq l\leq r\leq N$
• $\displaystyle\sum_{i=l}^{r}A_i = K$

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Given is a sequence of length $N$: $A=(A_1,A_2,\ldots,A_N)$, and an integer $K$.

How many of the contiguous subsequences of $A$ have the sum of $K$? In other words, how many pairs of integers $(l,r)$ satisfy all of the conditions below?

• $1\leq l\leq r\leq N$
• $\displaystyle\sum_{i=l}^{r}A_i = K$

Constraints

• $1\leq N \leq 2\times 10^5$
• $|A_i| \leq 10^9$
• $|K| \leq 10^{15}$
• All values in input are integers.

其中约30%的数据 $N \le 5000$。

Input

Input is given from Standard Input in the following format:

$N$ $K$

$A_1$ $A_2$ $\ldots$ $A_N$

Output

Print the answer.

Sample Input 1

6 5
8 -3 5 7 0 -4

Sample Output 1

3

$(l,r)=(1,2),(3,3),(2,6)$ are the three pairs that satisfy the conditions.

Sample Input 2

2 -1000000000000000
1000000000 -1000000000

Sample Output 2

0

There may be no pair that satisfies the conditions.

update @ 2024/3/10 10:08:53