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;
template <class T>
inline void in(T &x) {
  x = 0;
  char c = getchar();
  bool f = 0;
  while (!isdigit(c)) f |= (c == '-'), c = getchar();
  while (isdigit(c)) x = x * 10 + (c ^ '0'), c = getchar();
  f ? x = -x : 0;
}
template <class T>
inline void out(T x, const char c = '\n') {
  static short st[30];
  short m = 0;
  if (x < 0) {
    if (x == -2147483648) {
      printf("-2147483648");
      return;
    }
    putchar('-'), x = -x;
  }
  do st[++m] = x % 10, x /= 10;
  while (x);
  while (m) putchar(st[m--] | '0');
  putchar(c);
}
template <class T, class... Args>
inline void in(T &x, Args &...args) {
  in(x);
  in(args...);
}
template <class T, class... Args>
inline void out(const T &x, const Args &...args) {
  out(x, ' ');
  out(args...);
}
template <class T>
inline void prt(T a[], int n) {
  for (register int i = 0; i < n; ++i) out(a[i], ' ');
  putchar('\n');
}
template <class T>
inline void clr(T a[], int n) {
  memset(a, 0, sizeof(T) * n);
}
template <class T>
inline void clr(T *a, T *b) {
  memset(a, 0, sizeof(T) * (b - a));
}
template <class T>
inline bool ckmax(T &a, const T &b) {
  return a < b ? a = b, 1 : 0;
}
template <class T>
inline bool ckmin(T &a, const T &b) {
  return a > b ? a = b, 1 : 0;
}
namespace MOD_CALC {
const int md = 998244353, inv2 = (md + 1) / 2;
inline int add(const int a, const int b) {
  return a + b >= md ? a + b - md : a + b;
}
inline int sub(const int a, const int b) {
  return a - b < 0 ? a - b + md : a - b;
}
inline int mul(const int a, const int b) { return (long long)a * b % md; }
inline void inc(int &a, const int b) { (a += b) >= md ? a -= md : 0; }
inline void dec(int &a, const int b) { (a -= b) < 0 ? a += md : 0; }
inline int qpow(int a, int b) {
  int r = 1;
  for (; b; b >>= 1, a = mul(a, a))
    if (b & 1) r = mul(r, a);
  return r;
}
inline int qpow(int a, int b, const int p) {
  int r = 1;
  for (; b; b >>= 1, a = (long long)a * a % p)
    if (b & 1) r = (long long)r * a % p;
  return r;
}
inline int mdinv(const int a) { return qpow(a, md - 2); }
template <class... Args>
inline int add(const int a, const int b, const Args &...args) {
  return add(add(a, b), args...);
}
template <class... Args>
inline int mul(const int a, const int b, const Args &...args) {
  return mul(mul(a, b), args...);
}
}  // namespace MOD_CALC
using namespace MOD_CALC;
namespace i207M {
int n, K, L;
int f[4005][4005], g[4005][4005];
int fac[4005], ifac[4005];
signed main() {
  in(n, K, L);
  g[0][0] = 1;
  for (register int i = 1; i <= n + n; ++i)
    for (register int j = 0; j <= i; ++j) {
      if (j) {
        inc(g[i][j], g[i - 1][j - 1]);
        inc(f[i][j], add(f[i - 1][j - 1], (j - 1 >= K ? g[i - 1][j - 1] : 0)));
      }
      inc(g[i][j], mul(g[i - 1][j + 1], j + 1));
      inc(f[i][j], add(mul(f[i - 1][j + 1], j + 1),
                       (j + 1 >= K ? mul(g[i - 1][j + 1], j + 1) : 0)));
    }
  fac[0] = 1;
  for (register int i = 1; i <= n + n; ++i) fac[i] = mul(fac[i - 1], i);
  int ans = mul(f[n + n][0], mdinv(n + n + 1), mdinv(fac[n + n]), qpow(2, n),
                fac[n], L);
  out(ans);
  return 0;
}
}  // namespace i207M
signed main() {
  i207M::main();
  return 0;
}