#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;
inline pair<double,double> calc2(double X1,double Y1,double X2,double Y2){
	double k=(X2-X1)/(Y1-Y2),x=(X1+Y1)/2,y=(X2+Y2)/2;
	return make_pair(k,y-k*x);
}
inline pair<double,double> calc1(pair<double,double> l1,pair<double,double> l2){
	double x=(l1.second-l2.second)/(l2.first-l1.first);
	return make_pair(x,x*l1.first+l1.second);
}
inline double calc(pair<double,double> pr,int l,int r){
	double res=0;
	for(int i=l;i<=r;++i) res=max(res,sqrt((pr.first-X[i])*(pr.first-X[i])+(pr.second-Y[i])*(pr.second-Y[i])));
	return res;
}
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=30000,t=1;T--;++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_*t+X[id])/(t+1);y_=(y_*t+Y[id])/(t+1);
		}
		for(int k=i;k<=j;++k) for(int $=k;$<=j;++$)
			c[i][j]=min(c[i][j],calc(make_pair((X[k]+0ll+X[$])/2,(Y[k]+0ll+Y[$])/2),i,j));
		for(int k=i;k<=j;++k) for(int $=i;$<=j;++$) for(int _=i;_<=j;++_) if($-k&&_-k&&$-_)
			c[i][j]=min(c[i][j],calc(calc1(calc2(X[k],Y[k],X[$],Y[$]),calc2(X[k],Y[k],X[_],Y[_])),i,j));
	}
	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;
}