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.BufferedReader;
import java.io.FileNotFoundException;
import java.io.FileReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.StringTokenizer;



public class COVID {

	static ArrayList<Integer>[] adjList;






	static int[] fac;
	static int mod=998244353;

	static int pow(int b,long e, int mod) {
		int ans=1;
		b%=mod;
		while(e>0) {
			if((e&1)==1)
				ans=(int)((ans*1l*b)%mod);
			e>>=1;
			b=(int)((b*1l*b)%mod);
		}
		return ans;
	}
	static long ncr(int n , int r ) {
		long ans=fac[n];
		long de=((fac[n-r]*1l*fac[r])%mod);
		de=pow((int)de, mod-2, mod);
		return (ans*de)%mod;
	}

	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		PrintWriter pw =new PrintWriter(System.out);
		int n=sc.nextInt();
		long k=sc.nextLong();
		if(k>n-1) {
			pw.println(0);
			pw.flush();
			return;
		}
		fac=new int[n+1];
		fac[0]=1;
		for(int i=1;i<fac.length;i++)
			fac[i]=(int)((fac[i-1]*1l*(i%mod))%mod);
		
		int pop=n-(int)k;
		long ans=0;
		for(int i=0;i<=pop;i++) {
			long notPop= (ncr(pop,i)*pow(pop-i,n,mod))%mod;
			if(notPop<0) {
				System.out.println("here");
				
			}
			if(i%2==1)notPop*=-1;
			ans+=(notPop+mod);
			ans%=mod;
		}
		ans*=ncr(n,pop);
		ans%=mod;
		if(k!=0)
			ans=ans*2%mod;
		pw.println(ans);
		pw.flush();
		pw.close();
	}
	static long gcd(long a, long b) {
		return (b==0)?a:gcd(b,a%b);
	}
	static long lcm(long a, long b) {
		return a/gcd(a,b)*b;
	}
	public static int log(int n , int base) {
		int ans=0;
		while(n+1>base) {
			ans++;
			n/=base;
		}
		return ans;
	}
	static long square(long l) {
		return l*l;
	}





	static class Pair implements Comparable<Pair>{
		int  x;int y;

		public Pair(int a,int b) {
			this.x=a;y=b;
		}



		public int compareTo(Pair o) {
			return (x==o.x)?((y>o.y)?1:(y==o.y)?0:-1):((x>o.x)?1:-1);
		}


		@Override

		public int hashCode() {
			final int prime = 31;
			int result = 1;
			result = prime * result + x;
			result = prime * result + y;
			return result;
		}


		@Override
		public boolean equals(Object obj) {
			if (this == obj)
				return true;
			if (obj == null)
				return false;
			if (getClass() != obj.getClass())
				return false;
			Pair other = (Pair) obj;
			if (x != other.x)
				return false;
			if (y != other.y)
				return false;
			return true;
		}

	}





	static class Scanner {
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s) {
			br = new BufferedReader(new InputStreamReader(s));
		}
		public Scanner(String s) throws FileNotFoundException{	br = new BufferedReader(new FileReader(s));}

		public long[] nextLongArr(int n) throws IOException {
			long[] arr=new long[n];
			for(int i=0;i<n;i++)
				arr[i]=nextLong();
			return arr;
		}
		public int[] nextIntArr(int n) throws IOException {
			int[] arr=new int[n];
			for(int i=0;i<n;i++)
				arr[i]=nextInt();
			return arr;
		}
		public String next() throws IOException {
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine()," ,");
			return st.nextToken();
		}

		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}

		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}

		public String nextLine() throws IOException {
			return br.readLine();
		}


		public double nextDouble() throws IOException {
			String x = next();
			StringBuilder sb = new StringBuilder("0");
			double res = 0, f = 1;
			boolean dec = false, neg = false;
			int start = 0;
			if (x.charAt(0) == '-') {
				neg = true;
				start++;
			}
			for (int i = start; i < x.length(); i++) {
				if (x.charAt(i) == '.') {
					res = Long.parseLong(sb.toString());
					sb = new StringBuilder("0");
					dec = true;
				} else {
					sb.append(x.charAt(i));
					if (dec)
						f *= 10;
				}
				if (sb.length() == 18) {
					res += Long.parseLong(sb.toString()) / f;
					sb = new StringBuilder("0");
				}
			}
			res += Long.parseLong(sb.toString()) / f;
			return res * (neg ? -1 : 1);
		}

		public boolean ready() throws IOException {
			return br.ready();
		}

	}

	public static void shuffle(int[] a) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int r = i + (int) (Math.random() * (n - i));
			int tmp = a[i];
			a[i] = a[r];
			a[r] = tmp;
		}
	}
}
