#include<cstdio>
#include<cmath>
#include<iostream>
using namespace std;
const int o=2010,v1=233811181,v2=(1ll<<31)-1;const double inf=1e18;
int n,K,X[o],Y[o];double f[o][o],c[o][o],x_,y_,mx,v;
int main(){
	scanf("%d%d%d",&n,&K,&X[1]);
	for(int i=1;i<=n;++i){
		if(i>1) X[i]=(Y[i-1]*1ll*v1+1)%v2;
		Y[i]=(X[i]*1ll*v1+1)%v2;f[0][i]=inf;
	}
	for(int i=1;i<=n;++i) for(int j=i;j<=n;++j) c[i][j]=sqrt((X[i]-X[j])*1ll*(X[i]-X[j])+(Y[i]-Y[j])*1ll*(Y[i]-Y[j]))/2;
	for(int i=n;i;--i) for(int j=i;j<=n;++j) c[i][j]=max(c[i][j],c[i+1][j]);
	for(int i=1;i<=n;++i) for(int j=i;j<=n;++j) c[i][j]=max(c[i][j],c[i][j-1]);
	for(int i=1;i<=n;++i) for(int j=i,id;j<=n&&j<i+7;++j){
		c[i][j]=inf;
		if(j==i) x_=X[i],y_=Y[i];
		for(int T=7500;T--;){
			id=j;mx=0;
			for(int k=i;k<=j;++k) if((v=(x_-X[k])*1ll*(x_-X[k])+(y_-Y[k])*1ll*(y_-Y[k]))>mx) mx=v,id=k;
			c[i][j]=min(c[i][j],sqrt(mx));x_=(x_*10000+X[id])/10001;y_=(y_*10000+Y[id])/10001;
		}
	}
	for(int i=1;i<=K;++i) for(int j=1;j<=n;++j){
		f[i][j]=inf;
		for(int k=j,lim=n/K*50;k&&k>j-lim;--k) f[i][j]=min(f[i][j],f[i-1][k-1]+c[k][j]);
	}
	printf("%lf",f[K][n]);
	return 0;
}