Find the number of binary matrixes with $n$ rows and $m$ columns that there are at most $2$ ones in each row and column, modulo $998\,244\,353$.
Input
The first line of the input contains two integers $n$ and $m$ ($1 \leq n,m \leq 10^6$).
Output
Output a single line with a single integer, indicating the answer modulo $998\,244\,353$
Examples
Input
1 3
Output
7
Input
100 500
Output
528412063
Scoring
- Subtask 1 (10 points): $n,m \leq 100$
- Subtask 2 (10 points): $n,m \leq 10^3$
- Subtask 3 (25 points): $n,m \leq 10^4$
- Subtask 4 (30 points): $n,m \leq 10^5$
- Subtask 5 (15 points): $n = m$
- Subtask 6 (10 points): No additional constraints.