#include "bits/stdc++.h"
#define endl '\n'
#define f first
#define s second
#define pb push_back
#define mp make_pair
#define all(x) begin(x), end(x)
#define sz(x) (int)(x).size()
#define rep(i, a, b) for (int i = (a); i < (b); ++i)
std::mt19937 rng((int) std::chrono::steady_clock::now().time_since_epoch().count());
using namespace std;
#define int long long
 
#define dbg_loc() cerr << __PRETTY_FUNCTION__ << " : " << __LINE__ << "\n"
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p){ 
	return os << '(' << p.first << ", " << p.second << ')'; 
}
template<typename T_container,typename T=typename enable_if<!is_same<T_container,string>::value, typename T_container::value_type>::type> 
ostream& operator<<(ostream &os, const T_container &v){ 
	os << '{'; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << '}'; 
}
void dbg_out() { cerr << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T){ 
	cerr << ' ' << H; 
	dbg_out(T...); 
}
#define LOCAL
#define LOCAL
#ifdef LOCAL 
#define dbg(...) cerr<<"(" << #__VA_ARGS__<<"):" , dbg_out(__VA_ARGS__) , cerr << endl
#else
#define dbg(...)
#endif
#define per(i, a, b) for(int i = b-1; i>=a ; i--)
#define trav(a, x) for(auto& a : x)
#define allin(a , x) for(auto a : x)
typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;
// ll mod = (1000000007LL);
// inline ll Mod(ll a, ll b){return (a%b);}
// inline ll poww(ll a, ll b){ll res = 1;while (b > 0){if(b & 1) res = (res * a)%mod;a = (a * a)%mod;b >>= 1;}return res;}
ll gcd (ll a, ll b) { while (b) { a %= b,swap(a, b);}return a;}
void read(vector<int> &w, int n){w.resize(n);for(int i = 0; i < n; i++) cin>>w[i];}
void print(vector<int> &w){for(int i =0; i < sz(w); i++){if(i == sz(w) - 1) cout<<w[i]<<"\n";else cout<<w[i]<<" ";}}
 
///CUIDADO COM MAXN
#define N 50010 // 1E6
const int B =233811181;
const int mod = (1LL<<31) - 1;

int n, k, x[N], y[N];
int x1;
template <class T> int sgn(T x) { return (x > 0) - (x < 0); }
template<class T>
struct Point {
	typedef Point P;
	T x, y;
	explicit Point(T x=0, T y=0) : x(x), y(y) {}
	bool operator<(P p) const { return tie(x,y) < tie(p.x,p.y); }
	bool operator==(P p) const { return tie(x,y)==tie(p.x,p.y); }
	P operator+(P p) const { return P(x+p.x, y+p.y); }
	P operator-(P p) const { return P(x-p.x, y-p.y); }
	P operator*(T d) const { return P(x*d, y*d); }
	P operator/(T d) const { return P(x/d, y/d); }
	T dot(P p) const { return x*p.x + y*p.y; }
	T cross(P p) const { return x*p.y - y*p.x; }
	T cross(P a, P b) const { return (a-*this).cross(b-*this); }
	T dist2() const { return x*x + y*y; }
	long double dist() const { return sqrt((long double)dist2()); }
	// angle to x-axis in interval [-pi, pi]
	long double angle() const { return atan2(y, x); }
	P unit() const { return *this/dist(); } // makes dist()=1
	P perp() const { return P(-y, x); } // rotates +90 degrees
	P normal() const { return perp().unit(); }
	// returns point rotated 'a' radians ccw around the origin
	P rotate(long double a) const {
		return P(x*cos(a)-y*sin(a),x*sin(a)+y*cos(a)); }
	friend ostream& operator<<(ostream& os, P p) {
		return os << "(" << p.x << "," << p.y << ")"; }
};
typedef Point<long double> P;
long double ccRadius(const P& A, const P& B, const P& C) {
	return (B-A).dist()*(C-B).dist()*(A-C).dist()/
			abs((B-A).cross(C-A))/2;
}
P ccCenter(const P& A, const P& B, const P& C) {
	P b = C-A, c = B-A;
	return A + (b*c.dist2()-c*b.dist2()).perp()/b.cross(c)/2;
}

pair<P, long double> mec(vector<P> ps) {
	shuffle(all(ps), mt19937(time(0)));
	P o = ps[0];
	long double r = 0, EPS = 1 + 1e-8;
	rep(i,0,sz(ps)) if ((o - ps[i]).dist() > r * EPS) {
		o = ps[i], r = 0;
		rep(j,0,i) if ((o - ps[j]).dist() > r * EPS) {
			o = (ps[i] + ps[j]) / 2;
			r = (o - ps[i]).dist();
			rep(k,0,j) if ((o - ps[k]).dist() > r * EPS) {
				o = ccCenter(ps[i], ps[j], ps[k]);
				r = (o - ps[i]).dist();
			}
		}
	}
	return {o, r};
}

vector<P> pts;
long double cost2[2010][2010];

struct DP{
	int n ;
	long double inf; 
	vector<long double> dp[2];
	DP(int n , long double inf) : n(n) , inf(inf) {dp[0] = vector<long double>(n+1) , dp[1] = vector<long double>(n+1);}
	long double cost(int i,int j){
		assert(i<=j);
		return cost2[i][j];
	}
	// compute dp_cur[l], ... dp_cur[r] (inclusive) 
	void compute(int l, int r, int optl, int optr){
	    if (l > r) return;
	    int mid = l + (r-l)/2;
	    pair<long double, int> best = {inf, -1}; // se for maximizar muda pra -inf
	    rep(k,optl,min(mid,optr)+1){
	        best = min(best, { dp[0][k-1] + cost(k,mid), k});
	    }
	    dp[1][mid] = best.first; int opt = best.second;
	    compute(l, mid - 1, optl, opt);
	    compute(mid + 1, r, opt, optr);
	}
	void solve(int k){
		rep(i,1,n+1){
			dp[0][i] = cost(1,i);
			// dbg(dp[0][i]);
		}
		rep(i,2,k+1){
			rep(j,i,n+1) dp[1][j] = inf;
			compute(i,n,i,n) ;
			swap(dp[0] , dp[1]);
		}
	}
};

long double pica[2010][2010];
vi caras[N];
int32_t main(){
	ios::sync_with_stdio(false); cin.tie(0);
	cin>>n>>k>>x1;
	pts.resize(n);
	x[1] = x1%mod;
	y[1] = (x1*B + 1)%mod;
	pts[0] = P(x[1], y[1]);
	rep(i,2,n+1){
		x[i] = (y[i-1] * B + 1) % mod;
		y[i] = (x[i]*B + 1) %mod;
		pts[i-1] = P(x[i], y[i]);
	}

	rep(ini, 0, n){
		vector<P> ps;
		rep(i, ini, n) ps.pb(pts[i]);
		P o = ps[0];
		long double r = 0, EPS = 1 + 1e-8;
		long double old = -1.0;
		vi changes;
		rep(i,0,sz(ps)){
			if ((o - ps[i]).dist() > r * EPS) {
				o = ps[i], r = 0;
				rep(j,0,i) if ((o - ps[j]).dist() > r * EPS) {
					o = (ps[i] + ps[j]) / 2;
					r = (o - ps[i]).dist();
					rep(k,0,j) if ((o - ps[k]).dist() > r * EPS) {
						o = ccCenter(ps[i], ps[j], ps[k]);
						r = (o - ps[i]).dist();
					}
				}
				if(abs(r - old) > EPS){
					changes.pb(i+ini+1);
				}
				old=r;
			}
			int fim = ini + i;
			cost2[ini+1][fim+1] = r;
		}
		// caras[ini+1].pb(n);
		for(auto j: changes){
			caras[ini+1].pb(j);
			assert(j >= ini+1);
			if(j-1 >= ini+1 and j-1 <= n){
				caras[ini+1].pb(j-1);
			}
			if(j+1 >= ini+1 and j+1 <= n) caras[ini+1].pb(j+1);
		}
		sort(all(caras[ini+1])); caras[ini+1].erase(unique(all(caras[ini+1])), caras[ini+1].end());
	}

	// k * n * X <= 2e8
	// X = 2e8/(n*k)
	int X = 2e8/(n*k);
	for(int i = 1; i<=n;i++) pica[i][1] = cost2[i][n];

	for(int q = 2;q<=k;q++){
		for(int i =n;i >= 1;i--){
			pica[i][q] = 2e19;
			for(int j: caras[i]){
				pica[i][q] = min(pica[i][q], pica[j+1][q-1] + cost2[i][j]);
				// dbg(i,j,cost2[i][j]);
				assert(j>=i);
			}
		}
	}

	cout<<setprecision(20)<<"\n";
	// DP dp(n, 2e18);
	// dp.solve(k);
	// cout<<dp.dp[0][n]<<"\n";
	cout<<pica[1][k]<<"\n";
}