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.