被 EI 加 0 了 - 問題

#1603. 被 EI 加 0 了

統計

この問題は以下のコンテストで使用されています：

Elegia's Forgotten Hill

This problem is prepared by Elegia and xtqqwq .

给定 $n,m$ 。

求有多少个不同的正整数序列 $a_1,a_2,\dots,a_n$ ，使得对任意 $1\leq i\leq n$ 有 $1\leq a_i\leq m$ 且不存在 $1\leq i < j\leq n$ 满足 $\max\limits_{k=1}^i a_k=\min\limits_{k=j}^n a_k$ ，对 $998244353$ 取模。

输入格式

第一行一个正整数 $T$ ，代表测试组数。

接下来 $T$ 行，每行包含两个正整数 $n,m$ 。

输出格式

$T$ 行，每行一个正整数，代表这组数据的答案，对 $998244353$ 取模。

样例数据

样例输入

样例输出

2
12
7500

子任务

对于 $50\%$ 的数据，保证 $n\le 50$。

对于 $100\%$ 的数据，保证 $1\le T\le 10^5, 1\le n\le 300, 1\le m \le 10^9$。

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