Two Histograms

We have a square grid with N rows and M columns. Takahashi will write an integer in each of the squares, as follows:

• First, write 0 in every square.
• For each i=1,2,...,N, choose an integer k_i (0\leq k_i\leq M), and add 1 to each of the leftmost k_i squares in the i-th row.
• For each j=1,2,...,M, choose an integer l_j (0\leq l_j\leq N), and add 1 to each of the topmost l_j squares in the j-th column.

Now we have a grid where each square contains 0, 1, or 2. Find the number of different grids that can be made this way, modulo 998244353. We consider two grids different when there exists a square with different integers.

Constraints

• 1 \leq N,M \leq 5\times 10^5
• N and M are integers.

Input

Input is given from Standard Input in the following format:

N M

Output

Print the number of different grids that can be made, modulo 998244353.

Examples

Input

1 2

Output

8

Input

2 3

Output

234

Input

10 7

Output

995651918

Input

314159 265358

Output

70273732

inputFormat

Input

Input is given from Standard Input in the following format:

N M

outputFormat

Output

Print the number of different grids that can be made, modulo 998244353.

Examples

Input

1 2

Output

8

Input

2 3

Output

234

Input

10 7

Output

995651918

Input

314159 265358

Output

70273732

样例

10 7

995651918