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.*;
import java.math.*;

public class E {
    static final boolean RUN_TIMING = false;
    static PushbackReader in = new PushbackReader(new BufferedReader(new InputStreamReader(System.in)), 1024);
    static PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    final long MOD = 998244353;
    long[] fact = new long[200001];
    long[] invFact = new long[200001];

    public void go() throws IOException {
        // in = new PushbackReader(new BufferedReader(new FileReader(new File("test.txt"))), 1024);
        // out = new PrintWriter(new FileWriter(new File("output.txt")));
        int n = ipar();
        long kk = lpar();
        if (kk >= n) {
            out.println(0);
            return;
        }
        int k = (int)kk;
        fact[0] = 1;
        invFact[0] = 1;
        for (int i = 1; i < fact.length; i++) {
            fact[i] = fact[i-1] * i % MOD;
            invFact[i] = invFact[i-1] * inverse(i) % MOD;
        }
        int c = n-k;
        long ans = 0;
        for (int i = 0; i <= c; i++) {
            long contrib = i % 2 == 0 ? 1 : -1;
            contrib *= nck(c, i);
            contrib %= MOD;
            contrib *= modPow(c-i, n);
            contrib %= MOD;
            ans += contrib + MOD;
            ans %= MOD;
            // out.println("   " + contrib);
        }
        ans *= nck(n, k);
        ans %= MOD;
        if (k != 0) {
            ans *= 2;
            ans %= MOD;
        }
        out.println(ans);
    }

    public long nck(int n, int k) {
        return fact[n] * invFact[k] % MOD * invFact[n-k] % MOD;
    }

    public long inverse(long x) {
        return modPow(x, MOD-2);
    }

    public long modPow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 0) {
            return modPow(a*a%MOD, b/2);
        }
        return modPow(a*a%MOD, b/2) * a % MOD;
    }

    public int ipar() throws IOException {
        return Integer.parseInt(spar());
    }

    public int[] iapar(int n) throws IOException {
        int[] arr = new int[n];
        for (int i = 0; i < n; i++) {
            arr[i] = ipar();
        }
        return arr;
    }

    public long lpar() throws IOException {
        return Long.parseLong(spar());
    }

    public long[] lapar(int n) throws IOException {
        long[] arr = new long[n];
        for (int i = 0; i < n; i++) {
            arr[i] = lpar();
        }
        return arr;
    }

    public double dpar() throws IOException {
        return Double.parseDouble(spar());
    }

    public String spar() throws IOException {
        StringBuilder sb = new StringBuilder(1024);
        int c;
        do {
            c = in.read();
        } while (Character.isWhitespace(c) && c != -1);
        if (c == -1) {
            throw new NoSuchElementException("Reached EOF");
        }
        do {
            sb.append((char)c);
            c = in.read();
        } while (!Character.isWhitespace(c) && c != -1);
        while (c != '\n' && Character.isWhitespace(c) && c != -1) {
            c = in.read();
        }
        if (c != -1 && c != '\n') {
            in.unread(c);
        }
        return sb.toString();
    }

    public String linepar() throws IOException {
        StringBuilder sb = new StringBuilder(1024);
        int c;
        while ((c = in.read()) != '\n' && c != -1) {
            if (c == '\r') {
                continue;
            }
            sb.append((char)c);
        }
        return sb.toString();
    }

    public boolean haspar() throws IOException {
        String line = linepar();
        if (line.isEmpty()) {
            return false;
        }
        in.unread('\n');
        in.unread(line.toCharArray());
        return true;
    }

    public static void main(String[] args) throws IOException {
        long time = 0;
        time -= System.nanoTime();
        new E().go();
        time += System.nanoTime();
        if (RUN_TIMING) {
            System.out.printf("%.3f ms%n", time/1000000.0);
        }
        out.flush();
        in.close();
    }
}
