#D12002. Count the Arrays
Count the Arrays
Count the Arrays
Your task is to calculate the number of arrays such that:
- each array contains n elements;
- each element is an integer from 1 to m;
- for each array, there is exactly one pair of equal elements;
- for each array a, there exists an index i such that the array is strictly ascending before the i-th element and strictly descending after it (formally, it means that a_j < a_{j + 1}, if j < i, and a_j > a_{j + 1}, if j ≥ i).
Input
The first line contains two integers n and m (2 ≤ n ≤ m ≤ 2 ⋅ 10^5).
Output
Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo 998244353.
Examples
Input
3 4
Output
6
Input
3 5
Output
10
Input
42 1337
Output
806066790
Input
100000 200000
Output
707899035
Note
The arrays in the first example are:
- [1, 2, 1];
- [1, 3, 1];
- [1, 4, 1];
- [2, 3, 2];
- [2, 4, 2];
- [3, 4, 3].
inputFormat
Input
The first line contains two integers n and m (2 ≤ n ≤ m ≤ 2 ⋅ 10^5).
outputFormat
Output
Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo 998244353.
Examples
Input
3 4
Output
6
Input
3 5
Output
10
Input
42 1337
Output
806066790
Input
100000 200000
Output
707899035
Note
The arrays in the first example are:
- [1, 2, 1];
- [1, 3, 1];
- [1, 4, 1];
- [2, 3, 2];
- [2, 4, 2];
- [3, 4, 3].
样例
100000 200000
707899035