Submission #60400945

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Source Code Expand

/*
  Author: Denys Smirnov
  Time: 2024-12-02 17:45:06
*/

#include <iomanip>
#include "bits/stdc++.h"

#ifdef DENDI239
#define D                                                                      \
  for (bool _flag_dendi239 = true; _flag_dendi239; _flag_dendi239 = false)
#else
#define D while (false)
#endif

using namespace std;

signed main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);

  int n, x;
  cin >> n >> x;

  vector<int> ps(n);
  for (auto &p : ps)
    cin >> p;

  vector<double> in_level(n + 1, 0.0);
  in_level[0] = 1.;

  for (int i = 0; i < n; ++i) {
    const double p = ps[i] / 100.;
    for (int j = n; j > 0; --j)
      in_level[j] = (1 - p) * in_level[j] + p * in_level[j - 1];
    in_level[0] = (1 - p) * in_level[0];
  }

  vector<double> out_level(x + 1, 0.0);
  for (int i = 1; i <= x; ++i) {
    out_level[i] = 1;
    for (int j = max(0, i - n); j < i; ++j)
      out_level[i] += in_level[i - j] * out_level[j];
    out_level[i] /= 1 - in_level[0];
  }

  cout << setprecision(10) << fixed << out_level[x] << "\n";
}

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