#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return true; } return false; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return true; } return false; }
#define vi vector<int>
#define vl vector<ll>
#define vii vector<pair<int,int>>
#define vll vector<pair<ll,ll>>
#define vvi vector<vector<int>>
#define vvl vector<vector<ll>>
#define vvii vector<vector<pair<int,int>>>
#define vvll vector<vector<pair<ll,ll>>>
#define vst vector<string>
#define pii pair<int,int>
#define pll pair<ll,ll>
#define pb push_back
#define all(x) (x).begin(),(x).end()
#define mkunique(x) sort(all(x));(x).erase(unique(all(x)),(x).end())
#define fi first
#define se second
#define mp make_pair
#define si(x) int(x.size())
const int mod=998244353,MAX=300005,INF=15<<26;

#define ld _Float128
ld dp[MAX][153];

pair<ld,ld> db[77];

int main(){
    
    std::ifstream in("text.txt");
    std::cin.rdbuf(in.rdbuf());
    cin.tie(0);
    ios::sync_with_stdio(false);
    
    ll N,K;
    double ppp;
    ld P;cin>>N>>K>>ppp;
    P=ppp;
    ll pp=roundl(ppp*10000),qq=10000-pp,rr=10000;
    chmin(K,150LL);
    
    for(int j=0;j<=K;j++) dp[N][j]=0;
    dp[0][0]=0;
    for(int i=N-1;i>=0;i--){
        dp[0][0]+=1.0;
        dp[0][0]/=qq;
        dp[0][0]*=rr;
    }
    for(int i=N-1;i>=1;i--){
        dp[i][0]=(dp[i+1][0]*qq+dp[0][0]*pp+rr)/rr;
    }
    //cout<<fixed<<setprecision(25)<<dp[0][0]<<endl;
    
    for(int j=1;j<=K;j++){
        for(int i=N-1;i>=0;i--){
            if(dp[i+1][j]<1e5){
                long double s=((long double)(dp[i+1][j])*(qq)+(long double)(dp[i][j-1])*(pp))/(long double)rr+1;
                dp[i][j]=s;
            }else{
                dp[i][j]=(dp[i+1][j]*qq+dp[i][j-1]*pp+rr)/rr;
            }
        }
        ld l=dp[0][j-1]/2.2,r=dp[0][j-1]*1.2;
        for(int q=0;q<130;q++){
            ld m=(l+r)/2;
            int L=0,R=N;
            while(R-L>1){
                int M=(L+R)/2;
                if(dp[M][j-1]<m) R=M;
                else L=M;
            }
            db[0]=mp((ld)(qq)/rr,(ld)(m*pp)/rr+1);
            for(int s=1;s<=40;s++){
                auto [a,b]=db[s-1];
                db[s]=mp(a*a,a*b+b);
            }
            ld s=dp[R][j];
            int cn=L+1;
            for(int t=0;t<=20;t++){
                if(cn&(1<<t)){
                    s=db[t].fi*s+db[t].se;
                }
            }
            if(s>m) l=m;
            else r=m;
        }
        ld m=(l+r)/2;
        ld ad=m*pp/rr+1;
        for(int i=N-1;i>=0;i--){
            if(dp[i][j-1]>m){
                if(dp[i+1][j]<1e5&&ad<1e5){
                    long double s=((long double)(dp[i+1][j])*qq/(long double)rr+(ld)(ad));
                    dp[i][j]=s;
                }else{
                    dp[i][j]=dp[i+1][j]*qq/rr+ad;
                }
            }
        }
        //for(int i=0;i<=N;i++) cout<<dp[i][j]<<endl;
        //cout<<fixed<<setprecision(25)<<(l+r)/2<<endl;
    }
    
    cout<<fixed<<setprecision(25)<<(long double)(dp[0][K])<<endl;
}