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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastScanner in = new FastScanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        F solver = new F();
        solver.solve(1, in, out);
        out.close();
    }

    static class F {
        public void solve(int testNumber, FastScanner in, PrintWriter out) {
            int n = in.ni(), k = in.ni(), l = in.ni();
            int mod = 998244353;
            long[] invs = IntegerUtils.invs(2 * n + 3, mod);
            long[][] p = new long[2 * n + 1][n + 1];
            p[0][1] = 1; // first is always started
            for (int i = 1; i < 2 * n; i++) {
                int prevMaxRunning = Math.min(2 * n - i, i); // how many intervals max were running (covering)
                int maxRunning = Math.min(2 * n - i - 1, i + 1); // how many intervals max can be running
                for (int j = 0; j <= prevMaxRunning; j++) {
                    if (p[i - 1][j] != 0) {
                        if (j > 0) {
                            p[i][j - 1] = (p[i][j - 1] + p[i - 1][j] * j % mod * invs[2 * n - i] % mod) % mod; // close an interval
                        }
                        if (j < maxRunning) {
                            p[i][j + 1] = (p[i][j + 1] + p[i - 1][j] * (2 * n - i - j) % mod * invs[2 * n - i] % mod) % mod; // start a new interval
                        }
                    }
                }
            }
            long ans = 0;
            for (int i = 0; i < 2 * n; i++) {
                for (int j = k; j <= n; j++) {
                    if (p[i][j] == 0)
                        continue;
                    ans = (ans + p[i][j]) % mod;
                }
            }
            ans = ans * l % mod * invs[2 * n + 1] % mod;
            out.println(ans);
        }

    }

    static class FastScanner {
        private BufferedReader in;
        private StringTokenizer st;

        public FastScanner(InputStream stream) {
            in = new BufferedReader(new InputStreamReader(stream));
        }

        public String ns() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    String rl = in.readLine();
                    if (rl == null) {
                        return null;
                    }
                    st = new StringTokenizer(rl);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return st.nextToken();
        }

        public int ni() {
            return Integer.parseInt(ns());
        }

    }

    static class IntegerUtils {
        public static long[] invs(int n, long p) {
            long[] res = new long[n];
            res[1] = 1;
            for (int i = 2; i < n; i++) {
                res[i] = (p - (p / i) * res[(int) (p % i)] % p) % p;
            }
            return res;
        }

    }
}