Problem: Getting closer and closer to a mathematician, Serval becomes a university student on math major in Japari University. On the Calculus class, his teacher taught him how to calculate the expected length of a random subsegment of a given segment. Then he left a bonus problem as homework, with the award of a garage kit from IOI. The bonus is to extend this problem to the general case as follows.

You are given a segment with length l. We randomly choose n segments by choosing two points (maybe with non-integer coordinates) from the given segment equiprobably and the interval between the two points forms a segment. You are given the number of random segments n, and another integer k. The 2n endpoints of the chosen segments split the segment into (2n+1) intervals. Your task is to calculate the expected total length of those intervals that are covered by at least k segments of the n random segments.

You should find the answer modulo 998244353.

Input

First line contains three space-separated positive integers n, k and l (1≤ k ≤ n ≤ 2000, 1≤ l≤ 10^9).

Output

Output one integer — the expected total length of all the intervals covered by at least k segments of the n random segments modulo 998244353.

Formally, let M = 998244353. It can be shown that the answer can be expressed as an irreducible fraction p/q, where p and q are integers and q not ≡ 0 \pmod{M}. Output the integer equal to p ⋅ q^{-1} mod M. In other words, output such an integer x that 0 ≤ x < M and x ⋅ q ≡ p \pmod{M}.

Examples

Input


1 1 1


Output


332748118


Input


6 2 1


Output


760234711


Input


7 5 3


Output


223383352


Input


97 31 9984524


Output


267137618

Note

In the first example, the expected total length is \int_0^1 \int_0^1 |x-y|  dx dy = {1\over 3}, and 3^{-1} modulo 998244353 is 332748118.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main implements Runnable{
    public static void main(String[] args){
        //new Thread(null,new Main(),"Thread-1",1024*1024*10).start();
        new Main().run();
    }
    int mod=998244353;
    private void solve() throws Exception {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        int n=in.nextInt(),k=in.nextInt(),l=in.nextInt();
        long[]fac=new long[n+1];
        fac[0]=1;
        for(int i=1;i<=n;i++){
            fac[i]=fac[i-1]*i%mod;
        }
        long[][]dp=new long[2*n+1][2*n+2];
        dp[0][0]=1;
        for(int i=1;i<=2*n;i++){
            for(int j=0;j<=i;j++){
                if(j>0) dp[i][j]=(dp[i][j]+dp[i-1][j-1])%mod;
                dp[i][j]=(dp[i][j]+dp[i-1][j+1]*(j+1)%mod)%mod;
            }
        }
        long ans=0;
        for(int i=k;i<=2*n;i++){
            for(int j=k;j<=n;j++){
                ans=(ans+dp[i][j]*dp[2*n-i][j]%mod*fac[j]%mod)%mod;
            }
        }
        out.println(l*ans%mod*Pow(dp[2*n][0],mod-2)%mod*Pow(2*n+1,mod-2)%mod);
        out.flush();
    }
    long Pow(long a,long b){
        long ans=1;
        while(b>0){
            if((b&1)!=0)ans=(ans*a)%mod;
            a=(a*a)%mod;
            b>>=1;
        }
        return ans;
    }
    @Override
    public void run() {
        try {
            solve();
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    class InputReader{
        StreamTokenizer tokenizer;
        public InputReader(InputStream stream){
            tokenizer=new StreamTokenizer(new BufferedReader(new InputStreamReader(stream)));
            tokenizer.ordinaryChars(33,126);
            tokenizer.wordChars(33,126);
        }
        public String next() throws IOException {
            tokenizer.nextToken();
            return tokenizer.sval;
        }
        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }
        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
        public boolean hasNext() throws IOException {
            int res=tokenizer.nextToken();
            tokenizer.pushBack();
            return res!=tokenizer.TT_EOF;
        }
    }
}