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 block_size = 320;
const long long mod = 998244353;
const long long inf = 1e9 + 7;
const long double eps = 1e-9;
const double PI = atan(1) * 4;
template <typename T>
inline int sign(const T &a) {
  if (a < 0) return -1;
  if (a > 0) return 1;
  return 0;
}
string to_string(string s) { return '"' + s + '"'; }
string to_string(const char *s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
void debug_out() { cerr << endl; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
template <typename T, typename S>
inline bool upmin(T &a, const S &b) {
  return a > b ? a = b, 1 : 0;
}
template <typename T, typename S>
inline bool upmax(T &a, const S &b) {
  return a < b ? a = b, 1 : 0;
}
template <typename T>
inline void in(T &x) {
  x = 0;
  T f = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  x *= f;
}
long long twop(int x) { return 1LL << x; }
template <typename A, typename B>
inline void in(A &x, B &y) {
  in(x);
  in(y);
}
template <typename A, typename B, typename C>
inline void in(A &x, B &y, C &z) {
  in(x);
  in(y);
  in(z);
}
template <typename A, typename B, typename C, typename D>
inline void in(A &x, B &y, C &z, D &d) {
  in(x);
  in(y);
  in(z);
  in(d);
}
long long gcd(long long a, long long b) { return b == 0 ? a : gcd(b, a % b); }
long long fast(long long a, long long b) {
  long long ans = 1;
  while (b) {
    if (b & 1) {
      b--;
      ans = ans * a;
    } else {
      a = a * a;
      b /= 2;
    }
  }
  return ans;
}
long long fast(long long a, long long b, long long mod) {
  long long ans = 1;
  while (b) {
    if (b & 1) {
      b--;
      ans = ans * a % mod;
    } else {
      a = a * a % mod;
      b /= 2;
    }
  }
  return ans % mod;
}
template <typename T>
static T MOD(T a, T m) {
  a %= m;
  if (a < 0) a += m;
  return a;
}
template <typename T>
static T inverse(T a, T m) {
  a = MOD(a, m);
  if (a <= 1) return a;
  return MOD((1 - inverse(m, a) * m) / a, m);
}
const long long maxn = 100010;
long long fac[maxn], facinv[maxn], inv[maxn];
void init() {
  fac[0] = 1;
  for (long long i = 1; i < maxn; i++) fac[i] = i * (fac[i - 1]) % mod;
  facinv[maxn - 1] = inverse(fac[maxn - 1], mod);
  for (long long i = maxn - 2; i >= 0; i--) {
    facinv[i] = facinv[i + 1] * (i + 1) % mod;
  }
  inv[1] = 1;
  for (int i = 2; i < maxn; i++)
    inv[i] = (mod - (long long)mod / i * inv[mod % i] % mod);
}
long long combi(int n, int m) {
  if (n < 0 || m < 0 || n < m) return 0;
  return fac[n] * facinv[m] % mod * facinv[n - m] % mod;
}
namespace SOLVE {
long long two_power[100010];
long long u_coeff[4010];
long long p_coeff[4010];
void main() {
  init();
  two_power[0] = 1;
  for (long long i = 1; i < 100010; i++)
    two_power[i] = two_power[i - 1] * 2 % mod;
  long long n, k, l;
  in(n, k, l);
  for (long long i = k; i < n + 1; i++) {
    for (long long j = 0; j < n - i + 1; j++) {
      long long co = combi(n, i) * combi(n - i, j);
      if (j % 2 == 1) co *= -1;
      co %= mod;
      (u_coeff[i + j] += co) %= mod;
    }
  }
  for (long long i = 0; i < 4010; i++) {
    if (u_coeff[i]) {
      {};
    }
    u_coeff[i] = MOD(u_coeff[i], mod);
  }
  for (long long i = 0; i < n + 1; i++) {
    for (long long j = 0; j < i + 1; j++) {
      long long co = two_power[i] * combi(i, j) % mod * u_coeff[i] % mod;
      if ((i - j) % 2 == 1) co *= -1;
      (p_coeff[2 * i - j] += co) %= mod;
    }
  }
  for (long long i = 0; i < 4010; i++) {
    if (p_coeff[i]) {
      {};
    }
    p_coeff[i] = MOD(p_coeff[i], mod);
  }
  long long ans = 0;
  for (long long i = 0; i < 4010; i++) {
    if (p_coeff[i]) {
      ans += p_coeff[i] * inv[i + 1] % mod;
    }
  }
  ans %= mod;
  ans *= l;
  ans = MOD(ans, mod);
  cout << ans << endl;
}
}  // namespace SOLVE
signed main() {
  int t;
  t = 1;
  while (t--) {
    SOLVE::main();
  }
  return 0;
}