8647: Shattrath City

Velen calls a sequence "n-beautiful", if it satisfies the following three conditions:

1. Its length is larger than n.
2. Each element of the sequence is a positive integer $\le n$.
3. Each of its continuous subsequence of length n is NOT a permutation of 1,2...n

Velen takes inspiration from "n-beautiful" sequences, so he is interested in the number of "n-beautiful" sequences of length $m$.

Could you help him?

Since the answer can be very large, you only need to output the answer modulo 998244353.

The input consists of multiple test cases.

The first line contains an integer $(1\le T\le 4)$ denoting the number of test cases.

Each test case consists of only one line containing two integers n,m (3≤n<m≤2×105).

3
3 5
5 10
100000 200000

123
8001745
700646201