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]. 
import java.io.*;
import java.util.*;
import java.math.*;

 
 public class S	{
		static class Pair  implements Comparable<Pair> {
   int a;
   int b;
   public Pair(int x,int y){a=x;b=y;}
   public Pair(){}
   public int compareTo(Pair p1){
      return a+b-p1.a-p1.b;
   }
@Override
public int hashCode() {
	final int prime = 31;
	int result = 1;
	result = prime * result + a;
	result = prime * result + b;
	return result;
}
@Override
public boolean equals(Object obj) {
	Pair p = (Pair)obj;
	if (this.a==p.a && this.b==p.b)
		return true;
	else return false;
	
}
     
   
 }
static class TrieNode{
  TrieNode[]child;
  int w;
  boolean term;
  TrieNode(){
    child = new TrieNode[26];  
  }
}
  public static int gcd(int a,int b)
  {
    if(a<b)

      return gcd(b,a);
    if(b==0)
      return a;
    return gcd(b,a%b);
    
  }
  //static long ans = 0;
  static long mod = 998244353;//(long)(1e9+7);
   
    public static void main(String[] args) throws Exception {
       new Thread(null, null, "Anshum Gupta", 99999999) {
            public void run() {
                try {
                    solve();
                } catch(Exception e) {
                    e.printStackTrace();
                    System.exit(1);
                }
            }
        }.start();
    }

static long pow(long x,long y){
    if(y == 0)return 1;
    if(y==1)return x;
    long a = pow(x,y/2);
    a = (a*a)%mod;
    if(y%2==0){
        return a;
    }
    return (a*x)%mod;
}
static long my_inv(long x) {
	return pow(x,mod-2);
}
static long bin(int n,int r) {
	return (((fact[n]*inv_fact[n-r])%mod)*inv_fact[r])%mod;
}
static long mxx;
static int mxN = (int)(1e5+5);
static long[]fact,inv_fact;
 public static void solve() throws Exception {
   // solve the problem here
   MyScanner s = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out), true);
        int t = 1;//s.nextInt();
        mxx = (long)(1e18+5);
        while(t-->0){
        	int n = s.nextInt();
        	int m = s.nextInt();
        	if(n == 2) {
        		out.println("0");
        		break;
        	}
        	fact = new long[m+1];
        	inv_fact=new long[m+1];
        	fact[1] = inv_fact[1] = 1;
        	for(int i=2;i<=m;i++) {
        		fact[i] = (fact[i-1]*i)%mod;
        		inv_fact[i] = my_inv(fact[i]);
        	}
        	long ans = bin(m,n-1);
        	ans = (ans*(n-2))%mod;
        	ans = (ans * pow(2,n-3))%mod;
        	if(ans < 0)ans += mod;
        	out.println(ans);
        }
           
        out.flush();
}
 
     
 
 
 
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
 
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
 
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
 
        int nextInt() { return Integer.parseInt(next()); }
        long nextLong() { return Long.parseLong(next()); }
        double nextDouble() { return Double.parseDouble(next()); }
         
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
    //--------------------------------------------------------
}
