permutation 2

Problem Description

You are given three positive integers $N, x, y$. Please calculate how many permutations of $1 \sim N$ satisfies the following conditions (We denote the $i$-th number of a permutation by $p_i$):

1. $p_1 = x$
2. $p_N = y$
3. for all $1 \le i <N$, $|p_i - p_{i+1}| \le 2$

Input

The first line contains one integer $T$ denoting the number of tests. For each test, there is one line containing three integers $N, x, y$.

• $1 \le T \le 5000$
• $2 \le N \le 10^5$
• $1 \le x < y \le N$

Output

For each test, output one integer in a single line indicating the answer modulo $998244353$.

Sample Input

3

4 1 4

4 2 4

100000 514 51144

Sample Output

2

1

253604680

Source

2019 Multi-University Training Contest 5