#include <bits/stdc++.h>
#include <linux/limits.h>
#define sz(x) ((int)(x).size())
#define all(x) begin(x), end(x)
#ifdef memset0
#define log(...) fprintf(stderr, __VA_ARGS__)
#else
#define endl '\n'
#define log(...) (void(0))
#endif
using namespace std;
using ll = long long;
using lf = long double;
using ull = unsigned long long;
using lll = __int128;
const lf eps = 1e-10;
const int N = 100000, M = 1000;
int n, K;
int pos[N + 10];
lf f[N + 10][2], k[N + 10][2];
lf p;
bool le(lf x, lf y) { return x - y < eps; }
bool eq(lf x, lf y) { return abs(x - y) < eps; }
lf Getfn(int be, int j, int x) {
  // log("Get %d %d\n", j, x);
  int t = (j & 1);
  for (int i = be + 1; i <= n; ++i) {
    f[i][t] = k[i][t] = 0;
  }
  for (int i = be + 1; i <= n; ++i) {
    if (i <= x) f[i][t] = 1 + (1 - p) * f[i - 1][t] + p * f[i][t ^ 1];
    else
      f[i][t] = 1 + (1 - p) * f[i - 1][t], k[i][t] = (1 - p) * k[i - 1][t] + p;
  }
  f[n][t] /= (1 - k[n][t]);
  for (int i = x + 1; i < n; ++i) f[i][t] += k[i][t] * f[n][t];
  // for (int i = 1; i <= n; ++i) {
  //   log("%2.5Lf%c", f[i][j], " \n"[i == n]);
  // }
  return f[n][t];
}
int main() {
#ifdef memset0
  freopen("K.in", "r", stdin);
#endif
  cin.tie(0)->sync_with_stdio(0);
  cin >> n >> K >> p;
  K = min(K, min(1000, 8000000 / n + 2));
  Getfn(0, 0, 0);
  for (int j = 1; j <= K; ++j) {
    Getfn(0, j, pos[j - 1]);
    int l = pos[j - 1], r = n, mid;
    while (l < r) {
      mid = (l + r >> 1);
      if (le(Getfn(pos[j - 1], j, mid), Getfn(pos[j - 1], j, mid + 1))) r = mid;
      else
        l = mid + 1;
    }
    Getfn(pos[j - 1], j, l);
    pos[j] = l;
    // log("pos in %d=%d\n", j, pos[j]);
  }
  cout << fixed << setprecision(10) << f[n][K & 1] << "\n";
}