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;
long long dp[2005][2005][2];
int mod = 998244353;
long long f_pow(long long a, long long b) {
  long long res = 1, temp = a;
  while (b) {
    if (b & 1) res = res * temp % mod;
    temp = temp * temp % mod;
    b >>= 1;
  }
  return res;
}
int main() {
  int n, k, l;
  scanf("%d %d %d", &n, &k, &l);
  dp[0][0][0] = 1;
  if (k == 0) dp[0][0][1] = 1;
  for (int i = 1; i <= n; i++) {
    dp[i][0][0] = dp[i - 1][0][0] * (n - i + 1) % mod;
    dp[i][0][1] = dp[i - 1][0][1] * (n - i + 1) % mod;
    if (i >= k) {
      dp[i][0][1] += dp[i][0][0];
      dp[i][0][1] %= mod;
    }
    for (int j = 1; j <= i; j++) {
      dp[i][j][0] =
          (dp[i - 1][j][0] * (n - i + 1) + dp[i][j - 1][0] * (i - j + 1)) % mod;
      dp[i][j][1] =
          (dp[i - 1][j][1] * (n - i + 1) + dp[i][j - 1][1] * (i - j + 1)) % mod;
      if (i - j >= k) {
        dp[i][j][1] += dp[i][j][0];
        dp[i][j][1] %= mod;
      }
    }
  }
  long long temp = 1;
  for (int i = 1; i <= 2 * n + 1; i++) temp = temp * i % mod;
  for (int i = 1; i <= n; i++) {
    temp = temp * (mod + 1) / 2 % mod;
  }
  long long ans = dp[n][n][1];
  ans = ans * f_pow(temp, mod - 2) % mod;
  printf("%lld\n", ans * l % mod);
}