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 CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long MOD = 998244353;
const int MAXN = 2005;
int N, K;
long long L;
long long dp[2 * MAXN][MAXN][2];
long long bexp(long long b, int e = MOD - 2) {
  long long c = 1;
  while (e) {
    if (e & 1) {
      c = c * b % MOD;
    }
    b = b * b % MOD;
    e >>= 1;
  }
  return c;
}
int main() {
  cin >> N >> K >> L;
  memset(dp, 0, sizeof(dp));
  dp[0][1][0] = N;
  for (int i = 0; i < 2 * N; i++) {
    for (int j = 0; j <= N; j++) {
      for (int x = 0; x <= 1; x++) {
        if (dp[i][j][x]) {
          if (2 * N - (i + 1) > 1 - x + j) {
            dp[i + 1][j + 1][x] =
                (dp[i + 1][j + 1][x] +
                 dp[i][j][x] * (N - ((i + 1 - j - x) / 2 + j))) %
                MOD;
          }
          if (j) {
            dp[i + 1][j - 1][x] = (dp[i + 1][j - 1][x] + dp[i][j][x] * j) % MOD;
          }
          if (j >= K && !x) {
            dp[i + 1][j][1] = (dp[i + 1][j][1] + dp[i][j][x]) % MOD;
          }
        }
      }
    }
  }
  long long fact = 1;
  for (int i = 1; i <= 2 * N + 1; i++) {
    fact = fact * i % MOD;
  }
  long long ans =
      dp[2 * N][0][1] * bexp(2, N) % MOD * bexp(fact) % MOD * L % MOD;
  cout << ans << endl;
}