#ifdef NACHIA
#define _GLIBCXX_DEBUG
#else
#define NDEBUG
#endif
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
using u64 = unsigned long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
const i64 INF = 1001001001001001001;
template<typename A> void chmin(A& l, const A& r){ if(r < l) l = r; }
template<typename A> void chmax(A& l, const A& r){ if(l < r) l = r; }
using namespace std;

#include <cmath>

void testcase(){
    i64 n, k; cin >> n >> k;
    double p; cin >> p;
    cout.precision(20);
    cout << fixed;
    if(k >= 1000 || n*k >= 100000000){
        double a = n / (1 - p);
        cout << a << "\n";
        return;
    }
    vector<double> Q(n+1);
    for(int f=0; f<=n; f++) Q[f] = (1 - pow(1-p,f+1)) / p / pow(1-p,f) - 1;
    double ansK0 = Q[n];
    double q = 1.0 - p;
    vector<double> dp(n+1);
    for(int i=n-1; i>=0; i--) dp[i] = dp[i+1] * q + ansK0 * p + 1.0;
    //for(auto a : Q) cout << a << endl;
    //cout << endl;
    for(int a=1; a<=k; a++){
        vector<double> nx(n+1);
        for(int i=n-1; i>=0; i--){
            double val1 = q * nx[i+1] + p * dp[i] + 1.0;
            double val2 = nx[i+1] + p * Q[i+1] + 1.0;
            nx[i] = min(val1, val2);
        }
        swap(dp, nx);
    }
    cout << dp[0] << "\n";
}

int main(){
    ios::sync_with_stdio(false); cin.tie(nullptr);
    testcase();
    return 0;
}