#include <bits/stdc++.h>

using namespace std;
typedef long double ld;

const int N = 1e5 + 5;
const ld inf = 1e18;
ld f[N], g[N], qwq[N];

int main()
{
	int n, k, i, o;
	ld p, x, a, b;
	scanf("%d%d%Lf", &n, &k, &p);
	for(i = 1; i <= n; i++)
		f[i] = inf;
	++k;
	qwq[1] = p;
	for(i = 2; i <= n; i++)
		qwq[i] = qwq[i - 1] * (1 - p);
	k = min(k, 20000000 / n);
	while(k--)
	{
		for(i = 1; i <= n; i++)
			g[i] = f[i];
		for(i = n; i >= 1; i--)
			f[i] = 1 + (1 - p) * f[i + 1] + p * g[i];
		a = 1;
		b = f[1];
		x = inf;
		o = 0;
		for(i = 1; i <= n; i++)
		{
			a -= qwq[i];
			b -= qwq[i] * g[i];
			x = b / a;
			if(x >= g[i + 1])
				break;
		}
		o = i;
		a = b = 0;
		for(i = n; i >= 1; i--)
		{
			b = 1 + (1 - p) * b;
			a = (1 - p) * a;
			if(i > o)
				b += p * g[i];
			else
				a += p;
		}
		a = 1 - a;
		x = b / a;
		for(i = n; i >= 1; i--)
			f[i] = 1 + (1 - p) * f[i + 1] + p * min(x, g[i]);
	}
	printf("%.10Lf\n", f[1]);
	return 0;
}