/*FreeTimeLove's code.
Love has a nasty habit of disappearing over night.*/
#include<bits/stdc++.h>
namespace FRTMLV{
#define ll long long
#define LD long double
#define i7 __int128
#define re return
#define con continue
using namespace std;
template<class T>inline bool ckmin(T &a,T b){re b<a?a=b,1:0;}
template<class T>inline bool ckmax(T &a,T b){re a<b?a=b,1:0;}
const int N=2e3+5;
inline int rd(){
	int ans=0,f=0;
	char ch=getchar();
	while(ch<'0'||ch>'9')f^=(ch=='-'),ch=getchar();
	while(ch>='0'&&ch<='9')ans=(ans<<3)+(ans<<1)+(ch^48),ch=getchar();
	re f?-ans:ans;
}
mt19937 rnd(chrono::system_clock::now().time_since_epoch().count());
int n,K;
LD eps=1e-10;
struct node{
	LD x,y;
}a[N];
node operator +(node a,node b){re {a.x+b.x,a.y+b.y};}
node operator -(node a,node b){re {a.x-b.x,a.y-b.y};}
node operator *(node a,LD b){re {a.x*b,a.y*b};}
LD operator *(node a,node b){re a.x*b.y-b.x*a.y;}
inline LD dis(node a,node b){re sqrtl((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));}
inline node gtm(node a,node b){re (a+b)*0.5;}
inline node gto(node &a,node &b,node &c){
	node m1=gtm(a,b),m2=gtm(a,c);
	node k1={a.y-b.y,b.x-a.x},k2={a.y-c.y,c.x-a.x};
	node dm=m1-m2;
	LD dx=(dm*k2)/(k2*k1);
	re m1+(k1*dx);
}
LD dp[N][N];
void sol(int n){
	node o=a[n];
	LD r=0;
	for(int i=1;i<=K;i++)ckmin(dp[n][i],dp[n-1][i-1]);
	for(int i=n-1;i;i--){
		if(i+1<=K){
			ckmin(dp[n][i+1],dp[i][i-1]+r);
		}
		if(dis(o,a[i])<r+eps)con;
		for(int j=1;j<=K;j++)ckmin(dp[n][j],dp[i][j-1]+r);
		o=a[i],r=0;
		for(int j=n;j>i;j--){
			if(dis(o,a[j])<r+eps)con;
			o=gtm(a[i],a[j]),r=dis(o,a[i]);
			for(int k=n;k>j;k--){
				if(dis(o,a[k])<r+eps)con;
				o=gto(a[i],a[j],a[k]),r=dis(o,a[i]);
			}
		}
		for(int j=1;j<=K;j++)ckmin(dp[n][j],dp[i-1][j-1]+r);
	}
	for(int j=1;j<=K;j++)ckmin(dp[n][j],dp[0][j-1]+r);
}
inline ll inc(ll x){re (x*233811181+1)%((1ll<<31)-1);}
int main(){
	n=rd(),K=rd();
	a[1].x=rd(),a[1].y=inc(a[1].x);
	for(int i=2;i<=n;i++)a[i].x=inc(a[i-1].y),a[i].y=inc(a[i].x);
	for(int i=0;i<=n;i++)
		for(int j=0;j<=K;j++)dp[i][j]=0x3f3f3f3f3f3f3f3f;
	dp[0][0]=0;
	for(int i=1;i<=n;i++)sol(i);
	printf("%.12Lf\n",dp[n][K]);
//	for(int i=0;i<=n;i++){
//		for(int j=0;j<=K;j++)printf("%.3Lf ",dp[i][j]);puts("");
//	}
	re 0;
}
/*
3 2 1

100 23 213
*/
}int main(){re FRTMLV::main();}