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;
long long n, k, l, f[4010][2010], p[2010];
inline long long pow(long long x, long long y) {
  long long sum = 1;
  while (y) {
    if (y & 1) sum = sum * x % mod;
    x = x * x % mod;
    y >>= 1;
  }
  return sum;
}
int main() {
  cin >> n >> k >> l;
  l = l * pow(n << 1 | 1, mod - 2) % mod;
  p[0] = 1;
  for (long long i = 1; i <= n; i++) p[i] = i * p[i - 1] % mod;
  f[0][0] = 1;
  for (long long i = 0; i < (n << 1); i++) {
    for (long long j = min(n, i); ~j; j--) {
      f[i + 1][j + 1] = (f[i + 1][j + 1] + f[i][j]) % mod;
      if (j) f[i + 1][j - 1] = (f[i + 1][j - 1] + f[i][j] * j) % mod;
    }
  }
  long long ans = 0;
  for (long long i = 1; i <= (n << 1); i++) {
    for (long long j = k; j <= n; j++)
      ans = (ans + f[i][j] * f[(n << 1) - i][j] % mod * p[j]) % mod;
  }
  printf("%lld\n", ans * l % mod * pow(f[n << 1][0], mod - 2) % mod);
  return 0;
}