#line 1 "K.cpp"
// #pragma GCC target("avx2,avx512f,avx512vl,avx512bw,avx512dq,avx512cd,avx512vbmi,avx512vbmi2,avx512vpopcntdq,avx512bitalg,bmi,bmi2,lzcnt,popcnt")
// #pragma GCC optimize("Ofast")

#line 2 "/home/sigma/comp/library/template.hpp"

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
	if(x<y){ x=y; return true; }
	return false;
}
template<class T,class U> bool chmin(T& x, U y){
	if(y<x){ x=y; return true; }
	return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
    return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
  return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
	return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
	o<<"{";
	for(const T& v:vc) o<<v<<",";
	o<<"}";
	return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }

#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
void dmpr(ostream& os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
	os<<t<<" ~ ";
	dmpr(os,args...);
}
#define shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {";  \
	for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif

template<class D> D divFloor(D a, D b){
	return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
	return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
#line 5 "K.cpp"

using D = long double;
using P = pair<D,D>;
P operator+(const P& a, const P& b){return {a.first+b.first,a.second+b.second};}
P operator*(D a, const P& b){return {a*b.first,a*b.second};}

int main(){
	cin.tie(0);
	ios::sync_with_stdio(false);		//DON'T USE scanf/printf/puts !!
	cout << fixed << setprecision(20);

	int N,K; cin >> N >> K;
	D p; cin >> p;
	chmin(K, 10000000/N);
	V<D> prev(N+1);
	V<D> tmp(N+1);
	V<P> dp(N+1);	// a+bX, X = dp[N]
	rep(i,K+1){
		auto doit = [&](int t, bool fill) -> int {
			// j <= t なら使う
			dp[0] = P(0,0);
			rep1(j,N){
				dp[j] = P(1,0) + p * (j <= t ? P(prev[j],0) : P(0,1)) + (1-p) * dp[j-1];
			}
			D X = dp[N].fs / (1 - dp[N].sc);
			int actual_t = 0;
			rep1(j,N){
				if(prev[j] <= X) actual_t = j;
			}

			if(fill){
				rep(j,N+1) chmin(tmp[j], dp[j].fs + dp[j].sc * X);
			}

			return actual_t;
		};

		rep(j,N+1) tmp[j] = 1e100;
		if(i == 0){
			doit(-1, true);
		}else{
			int lb = 1, ub = N+1;
			while(ub-lb > 1){
				int t = (lb+ub)/2;
				int actual_t = doit(t, false);
				if(actual_t <= t) ub = t;
				else lb = t;
			}
			doit(lb, true);
			doit(ub, true);
		}
		swap(prev, tmp);
	}
	cout << prev[N] << endl;
}