#include <bits/stdc++.h>
#define x first
#define y second
using namespace std;
using ld=__float128;
//using ld=long double;
using pii=pair<int,int>;
using vi=vector<int>;
using ll=long long;
using vl=vector<ll>;
#define pb push_back
#define all(a) begin(a),end(a)

const int N=100010,MOD=1e9+7;
const char en='\n';
const ll LLINF=1ll<<60;

int n,k;
ld dp[310][N],p;
pair<ld,ld> id={1,0},po[N];

pair<ld,ld> mul(pair<ld,ld> a,pair<ld,ld> b) //*.x+.y
{
	return {a.x*b.x,a.y*b.x+b.y};
}

pair<ld,ld> pot(pair<ld,ld> a,int c)
{
	pair<ld,ld> an=id,cu=a;
	for (;c;c/=2)
	{
		if (c%2) an=mul(an,cu);
		cu=mul(cu,cu);
	}
	return an;
	//return {pow(a.x,(ld)c),a.y*(1-pow(a.x,(ld)c))/(1-a.x)};
}

int main()
{
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	cout<<fixed<<setprecision(15);
	long double pr;
	cin>>n>>k>>pr;
	p=pr;
	po[0]=id;
	for (int i=1;i<=n;++i) po[i]=mul(po[i-1],{1.L-p,1.L});
	//k=0
	auto re=po[n];
	//x=a*re.x+re.y*(px+1)
	//x(1-re.y*p)=a*re.x+re.y
	//x=(a*re.x+re.y)/(1-re.y*p)
	dp[0][0]=re.y/(1-re.y*p);
	for (int i=n-1;i>=1;--i) dp[0][i]=p*dp[0][0]+(1-p)*dp[0][i+1]+1;
	int md=n;
	for (int z=1;z<=k;++z)
	{
		ld mi=dp[0][0];
		int kak=md;
		for (int i=n-1;i>=0;--i)
		{
			ld a=(1-p)*dp[z][i+1]+p*dp[z-1][i]+1;
			ld nov0=(a*po[i].x+po[i].y)/(1-po[i].y*p);
			if (nov0<mi)
			{
				mi=nov0;
				kak=i;
			}
			dp[z][i]=a;
			//cout<<z<<' '<<i<<' '<<(long double)nov0<<en;
		}
		assert(kak!=n);
		//cout<<z<<' '<<kak<<en;
		md=kak;
		dp[z][0]=mi;
		for (int i=kak-1;i>=1;--i)
		{
			ld o2=p*dp[z][0]+(1-p)*dp[z][i+1]+1;
			dp[z][i]=o2;
		}
		if (mi<(n/(1-p))*(1+1e-10))
		{
			cout<<(long double)(n/(1-p))<<en;
			exit(0);
		}
		//cout<<(long double)(p*dp[z][0]+(1-p)*dp[z][1]+1)<<' '<<(long double)mi<<endl;
	}
	//for (int i=0;i<=k;++i,cout<<en) for (int j=0;j<=n;++j) cout<<(long double)dp[i][j]<<' ';
	cout<<(long double)dp[k][0]<<en;
	//cout<<(long double)(n/(1-p))<<en;
}