#include<cstdio>
#include<cmath>
#include<iostream>
using namespace std;
const int o=2010,v1=233811181,v2=(1ll<<31)-1;const double inf=1e18,eps=1e-6;
int n,K,X[o],Y[o],tp[o],st[o][o];double f[o][o],c[o][o],ox,oy,R;
inline pair<double,double> calc2(double X1,double Y1,double X2,double Y2){
	double k=(X2-X1)/(Y1-Y2),x=(X1+X2)/2,y=(Y1+Y2)/2;
	return make_pair(k,y-k*x);
}
inline void calc1(pair<double,double> l1,pair<double,double> l2,double&x,double&y){
	x=(l1.second-l2.second)/(l2.first-l1.first);y=x*l1.first+l1.second;
}
inline double dis(int t){return sqrt((ox-X[t])*(ox-X[t])+(oy-Y[t])*(oy-Y[t]));}
inline bool chk(int t){return dis(t)<R+eps;}
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){
		R=-1;
		for(int j=i;j;--j) if(!chk(j)){
			if(j<i) st[i][++tp[i]]=j+1,c[i][tp[i]]=R;
			ox=X[j];oy=Y[j];R=0;
			for(int k=i;k>j;--k) if(!chk(k)){
				ox=(X[j]+0.0+X[k])/2;oy=(Y[j]+0.0+Y[k])/2;R=dis(k);
				for(int $=i;$>k;--$)
					if(!chk($)) calc1(calc2(X[j],Y[j],X[k],Y[k]),calc2(X[j],Y[j],X[$],Y[$]),ox,oy),R=dis($);
			}
		}
		st[i][++tp[i]]=1;c[i][tp[i]]=R;
	}
	for(int i=1;i<=K;++i) for(int j=1;j<=n;++j){
		f[i][j]=inf;
		for(int k=1;k<=tp[j];++k) f[i][j]=min(f[i][j],f[i-1][st[j][k]-1]+c[j][k]);
	}
	printf("%lf",f[K][n]);
	return 0;
}