#include<bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,avx2,tune=native")
using namespace std;
inline int read(){
   int s=0,w=1;
   char ch=getchar();
   while(ch<'0'||ch>'9'){if(ch=='-')w=-1;ch=getchar();}
   while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
   return s*w;
}
// #define ld __float128
#define ld long double
ld f[501][100003];
int n=read(),m=read();
ld p;
ld pw[100003],ipw[100003];
void init()
{
	ld t=(1-pw[n])/p*ipw[n];
		for(int i=n-1; i>=0; --i)
			f[0][i]=p*t+(1-p)*f[0][i+1]+1;
}
signed main()
{
	if(n<=10000) m=min(m,500);
	else m=min(m,100);
	double p_;
	cin>>p_;
	p=p_;
	pw[0]=ipw[0]=1;
	for(int i=1; i<=n; ++i) pw[i]=pw[i-1]*(1-p);
	ld inv=1.0L/(1.0L-p);
	for(int i=1; i<=n; ++i) ipw[i]=ipw[i-1]*inv;
	init();
	for(int d=1; d<=m; ++d)
	{
		ld t=1e18;
		for(int i=n; i>=0; --i)
		{
			if(i!=n) f[d][i]=p*f[d-1][i]+(1-p)*f[d][i+1]+1;
			t=min(t,(1-pw[i])/p*ipw[i]+f[d][i]);
			// printf("%.1Lf\n",(long double)((1-pw[i])/(1-p)/pw[i]+f[d][i]));
		}
		// return 0;
		// printf("%.10Lf ",(long double)f[d][0]);
		for(int i=n-1; i>=0; --i)
			f[d][i]=p*min(t,f[d-1][i])+(1-p)*f[d][i+1]+1;
		// printf("%.10Lf\n",(long double)f[d][0]);
	}
	printf("%.10Lf\n",(long double)f[m][0]);
	return 0;
}