链接：https://codeforces.ml/contest/1312/problem/D

Your task is to calculate the number of arrays such that:

  • each array contains nn elements;
  • each element is an integer from 11 to mm;
  • for each array, there is exactly one pair of equal elements;
  • for each array aa, there exists an index ii such that the array is strictly ascending before the ii-th element and strictly descendingafter it (formally, it means that aj<aj+1aj<aj+1, if j<ij<i, and aj>aj+1aj>aj+1, if j≥ij≥i).

Input

The first line contains two integers nn and mm (2≤n≤m≤2⋅1052≤n≤m≤2⋅105).

Output

Print one integer — the number of arrays that meet all of the aforementioned conditions, taken modulo 998244353998244353.

Examples

input

Copy

3 4

output

Copy

6

input

Copy

3 5

output

Copy

10

input

Copy

42 1337

output

Copy

806066790

input

Copy

100000 200000

output

Copy

707899035

Note

The arrays in the first example are:

  • [1,2,1][1,2,1];
  • [1,3,1][1,3,1];
  • [1,4,1][1,4,1];
  • [2,3,2][2,3,2];
  • [2,4,2][2,4,2];
  • [3,4,3][3,4,3].

代码：

#include <bits/stdc++.h>
using namespace std;
const int mod=998244353;
long long n,m,s1,s2,ans;
long long qpow(long long a,long long b) 
{
	long long res=1;
	while(b) 
	{
		if(b&1) 
		{
			res=(res*a)%mod;
		}
		a=(a*a)%mod;
		b>>=1;
	}
	return res;
}
int main () 
{
	cin>>n>>m;
	s1=1;
	s2=1;
	for(int i=2;i<=n-2;i++) 
	{
		s1=(s1*2)%mod;
	}
	for(int i=1;i<=n-1;i++) 
	{
		s2=(s2*(m-i+1))%mod;
		s2=(s2*qpow(i,mod-2))%mod;
	}
	ans=(n-2)*s1%mod*s2%mod;
	cout<<ans;
	return 0;
}