Given an $n \times n$ grid, there are $q$ queries. Each query is of the form $(x, y)$, where $x \le y$. Starting from cell $(x, y)$, you can move from cell $(i,j)$ to cells $(i + 1, k)$ and $j \le k \le n$. However, you cannot move to cells with coordinates $(a, b)$ where $a > b$. Determine the number of ways to reach $(n, n)$ from $(x, y)$.
### Input
- The first line contains two integers $n, q$.
- The next $q$ lines, each containing two integers $x, y$, representing a query.
### Output
- For each query, print an integer representing the number of paths modulo $998244353$ from $(x, y)$ to $(n, n)$.
### Constraints
- $1 \le n,q \le 10^5$.
- $1 \le x \le y \le n$.
### Sample test
Input
```
5 3
2 4
1 1
1 3
```
Output:
```
3
14
9
```
