There are $m$ plates and $n$ apples. We want to place each apple into one of the $m$ plates, resulting in a total of $m^n$ possible configurations. An operation is defined as moving an apple to an adjacent plate. For a given configuration, the cost is defined as the minimum number of operations required to move all apples into the same plate. Calculate the sum of the costs over all $m^n$ configurations, modulo $998244353$.

Input

The input consists of a single line containing two integers $n$ and $m$ ($1 \le n \le 2 \times 10^5, 1 \le m \le 10^9$).

Output

Output a single integer representing the sum of the costs over all configurations, modulo $998244353$.

Examples

Input 1

2 3

Output 1

8

Input 2

3 3

Output 2

36