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 int MAXN = 4005;
int n, k, l;
long long fac[MAXN], finv[MAXN], f[MAXN][MAXN][2];
inline long long qpow(long long a, int b) {
  long long res = 1;
  for (; b; a = a * a % 998244353, b >>= 1)
    if (b & 1) res = res * a % 998244353;
  return res;
}
inline long long getInv(int x) { return qpow(x, 998244353 - 2); }
int main() {
  cin >> n >> k >> l;
  fac[0] = finv[0] = 1;
  for (int i = 1; i <= 2 * n + 1; i++)
    fac[i] = fac[i - 1] * i % 998244353,
    finv[i] = finv[i - 1] * getInv(i) % 998244353;
  f[0][0][0] = 1;
  for (int i = 1; i <= 2 * n + 1; i++)
    for (int j = 0; j <= i; j++)
      for (int p = 0; p <= 1; p++) {
        if (j >= k && p == 1)
          f[i][j][p] = (f[i][j][p] + f[i - 1][j][0]) % 998244353;
        if (j > 0 && i + j <= 2 * n + p)
          f[i][j][p] = (f[i][j][p] + f[i - 1][j - 1][p]) % 998244353;
        f[i][j][p] =
            (f[i][j][p] + f[i - 1][j + 1][p] * (j + 1) % 998244353) % 998244353;
      }
  cout << l * f[2 * n + 1][0][1] % 998244353 * fac[n] % 998244353 * qpow(2, n) %
              998244353 * finv[2 * n + 1] % 998244353
       << endl;
  return 0;
}