Two Arrays

题意翻译

给定一个长为 $n$ 的数组 $a$ 和一个长为 $m$ 的数组 $b$ ($m\leq n$) ，你要把 $a$ 分割为连续的 $m$ 段使得第 $i$ 段中的最小值恰为 $b_i$ ，求总方案数，对998244353取模。保证 $b$ 严格单调递增。

题目描述

You are given two arrays $ a_1, a_2, \dots , a_n $ and $ b_1, b_2, \dots , b_m $ . Array $ b $ is sorted in ascending order ( $ b_i < b_{i + 1} $ for each $ i $ from $ 1 $ to $ m - 1 $ ). You have to divide the array $ a $ into $ m $ consecutive subarrays so that, for each $ i $ from $ 1 $ to $ m $ , the minimum on the $ i $ -th subarray is equal to $ b_i $ . Note that each element belongs to exactly one subarray, and they are formed in such a way: the first several elements of $ a $ compose the first subarray, the next several elements of $ a $ compose the second subarray, and so on. For example, if $ a = [12, 10, 20, 20, 25, 30] $ and $ b = [10, 20, 30] $ then there are two good partitions of array $ a $ : 1. $ [12, 10, 20], [20, 25], [30] $ ; 2. $ [12, 10], [20, 20, 25], [30] $ . You have to calculate the number of ways to divide the array $ a $ . Since the number can be pretty large print it modulo 998244353.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ ( $ 1 \le n, m \le 2 \cdot 10^5 $ ) — the length of arrays $ a $ and $ b $ respectively. The second line contains $ n $ integers $ a_1, a_2, \dots , a_n $ ( $ 1 \le a_i \le 10^9 $ ) — the array $ a $ . The third line contains $ m $ integers $ b_1, b_2, \dots , b_m $ ( $ 1 \le b_i \le 10^9; b_i < b_{i+1} $ ) — the array $ b $ .

输出格式

In only line print one integer — the number of ways to divide the array $ a $ modulo 998244353.

输入输出样例

输入样例 #1

6 3
12 10 20 20 25 30
10 20 30

输出样例 #1

2

输入样例 #2

4 2
1 3 3 7
3 7

输出样例 #2

0

输入样例 #3

8 2
1 2 2 2 2 2 2 2
1 2

输出样例 #3

7