Calculate the number of ways to place n rooks on n × n chessboard so that both following conditions are met:

  * each empty cell is under attack; 
  * exactly k pairs of rooks attack each other. 



An empty cell is under attack if there is at least one rook in the same row or at least one rook in the same column. Two rooks attack each other if they share the same row or column, and there are no other rooks between them. For example, there are only two pairs of rooks that attack each other in the following picture:

<image> One of the ways to place the rooks for n = 3 and k = 2

Two ways to place the rooks are considered different if there exists at least one cell which is empty in one of the ways but contains a rook in another way.

The answer might be large, so print it modulo 998244353.

Input

The only line of the input contains two integers n and k (1 ≤ n ≤ 200000; 0 ≤ k ≤ (n(n - 1))/(2)).

Output

Print one integer — the number of ways to place the rooks, taken modulo 998244353.

Examples

Input


3 2


Output


6


Input


3 3


Output


0


Input


4 0


Output


24


Input


1337 42


Output


807905441
import java.io.*;
import java.util.*;

public class Main{
	static int mod=998244353;
	static long fastpow(long n,long ti) {
		 if (ti == 0) 
		        return 1l;
		if(ti%2==0) {
			long y=fastpow(n, ti/2);
			long k=y*y;
			k%=mod;
			return k;
		}
		else {
			long y=fastpow(n, ti/2);
			long k=((n*y)%mod)*y;
			k%=mod;
			return k;
		}
	}
	static long[]fac;
	
	public static long ncr(int n,int k) {
		if(n<k)return 0;
		long num=fac[(n)];
		long den=(fac[(n-k)]*fac[k])%mod;
		long ans=(num*fastpow(den,mod-2));
		return ans%mod;
	}
	public static void main(String[] args) throws Exception{
		PrintWriter pw=new PrintWriter(System.out);
		MScanner sc = new MScanner(System.in);
		fac=new long[(int)2e5+1];
		fac[0]=1;for(int i=1;i<fac.length;i++)fac[i]=(fac[i-1]*i)%mod;
		
		int n=sc.nextInt();long k=sc.nextLong();
		if(k>=n) {
			pw.println(0);
			pw.flush();
			return;
		}
		if(k==0) {
			pw.println(fac[(int)n]);
			pw.flush();
			return;
		}
		if(k==n-1) {
			pw.println(2*n);
			pw.flush();
			return;
		}
		//columns to fill with one rook
		int filledCols=(int)(n-k);
		
		long waysToChooseFilledCols=ncr(n, filledCols);
		
		long ans=0;
		
		for(int emptyCols=0;emptyCols<=filledCols;emptyCols++) {
			long waysToChoose=ncr(filledCols, emptyCols);
			long waysToFill=fastpow(filledCols-emptyCols, n);
			long val=(waysToChoose*waysToFill)%mod;
			
			if(emptyCols%2==1) {
				val*=-1;
			}
			ans=(ans+val+mod)%mod;
		}
		ans=(ans*waysToChooseFilledCols)%mod;
		
		//the same for rows
		ans=(ans*2)%mod;
		
		pw.println(ans);
		pw.flush();
	}
	static class MScanner {
		StringTokenizer st;
		BufferedReader br;
		public MScanner(InputStream system) {
			br = new BufferedReader(new InputStreamReader(system));
		}
 
		public MScanner(String file) throws Exception {
			br = new BufferedReader(new FileReader(file));
		}
 
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}
		public int[] intArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public long[] longArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public int[] intSortedArr(int n) throws IOException {
	        int[]in=new int[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public long[] longSortedArr(int n) throws IOException {
	        long[]in=new long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        shuffle(in);
	        Arrays.sort(in);
	        return in;
		}
		public Integer[] IntegerArr(int n) throws IOException {
	        Integer[]in=new Integer[n];for(int i=0;i<n;i++)in[i]=nextInt();
	        return in;
		}
		public Long[] LongArr(int n) throws IOException {
	        Long[]in=new Long[n];for(int i=0;i<n;i++)in[i]=nextLong();
	        return in;
		}
		public String nextLine() throws IOException {
			return br.readLine();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
 
		public char nextChar() throws IOException {
			return next().charAt(0);
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public boolean ready() throws IOException {
			return br.ready();
		}
 
		public void waitForInput() throws InterruptedException {
			Thread.sleep(3000);
		}
	}
	static void shuffle(int[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			int tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static void shuffle(long[]in) {
		for(int i=0;i<in.length;i++) {
			int idx=(int)(Math.random()*in.length);
			long tmp=in[i];
			in[i]=in[idx];
			in[idx]=tmp;
		}
	}
	static String arrToString(int[]x) {
		return Arrays.toString(x);
	}
	static String arrToString(long[]x) {
		return Arrays.toString(x);
	}
	static String arrToString(Integer[]x) {
		return Arrays.toString(x);
	}
	static String arrToString(Long[]x) {
		return Arrays.toString(x);
	}
}