#include <bits/stdc++.h>
//#define double long double
#define eps 1e-7
using namespace std;
const int N = 2001, T = 5e8;
const int Mod = 2147483647;
const int base = 233811181;
int Read() {
    int x = 0, f = 1;
    char ch = getchar();
    while (!isdigit(ch) && ch != '-')
        ch = getchar();
    if (ch == '-')
        f = -1, ch = getchar();
    while (isdigit(ch))
        x = (x << 3) + (x << 1) + ch - '0', ch = getchar();
    return (f == -1) ? -x : x;
}
int x[N], y[N];
double r;
struct point {
    double x, y;
} p[N], o;
double sqr(double x) { return x * x; }
double dis(point a, point b) {
    return sqrt(sqr(a.x - b.x) + sqr(a.y - b.y));
}
bool cmp(double a, double b) { return fabs(a - b) < eps; }

double s[N][N];

point geto(point a, point b, point c) {
    double a1, a2, b1, b2, c1, c2;
    point ans;
    a1 = 2 * (b.x - a.x), b1 = 2 * (b.y - a.y),
    c1 = sqr(b.x) - sqr(a.x) + sqr(b.y) - sqr(a.y);
    a2 = 2 * (c.x - a.x), b2 = 2 * (c.y - a.y),
    c2 = sqr(c.x) - sqr(a.x) + sqr(c.y) - sqr(a.y);
    if (cmp(a1, 0)) {
        ans.y = c1 / b1;
        ans.x = (c2 - ans.y * b2) / a2;
    } else if (cmp(b1, 0)) {
        ans.x = c1 / a1;
        ans.y = (c2 - ans.x * a2) / b2;
    } else {
        ans.x = (c2 * b1 - c1 * b2) / (a2 * b1 - a1 * b2);
        ans.y = (c2 * a1 - c1 * a2) / (b2 * a1 - b1 * a2);
    }
    return ans;
}

vector<int> v[2005];
double f[2005][2005];

double F(int k, int n) {
	if(n == 0)  return 1E18;
	if(k == 1)  return s[1][n];
	if(!cmp(f[k][n], 0))  return f[k][n];
	int len = v[n].size();
	double tmp = 1E18;
	for(int i = 0; i < len; i++) {
		int u = v[n][i];
		tmp = min(tmp, F(k - 1, u - 1) + s[u][n]);
	}
	return f[k][n] = tmp;
}

signed main() {
    int n = Read(), k = Read(); x[1] = Read();
    y[1] = (1ll * x[1] * base + 1) % Mod;
    p[1].x = x[1], p[1].y = y[1];
    for (int i = 2; i <= n; i++) {
        x[i] = (1ll * y[i - 1] * base + 1) % Mod;
        y[i] = (1ll * x[i] * base + 1) % Mod;
        p[i].x = x[i];
        p[i].y = y[i];
    }
    for (int l = n; l > 0; l--) {
        r = 0;
        o = p[l];
        for (int i = l; i <= n; i++) {
            if (dis(o, p[i]) < r || cmp(dis(o, p[i]), r)){
                s[l][i] = r;
                continue;
            }
            o.x = (p[i].x + p[l].x) / 2;
            o.y = (p[i].y + p[l].y) / 2;
            r = dis(p[i], p[l]) / 2;
            for (int j = l + 1; j < i; j++) {
                if (dis(o, p[j]) < r || cmp(dis(o, p[j]), r))
                    continue;
                o.x = (p[i].x + p[j].x) / 2;
                o.y = (p[i].y + p[j].y) / 2;
                r = dis(p[i], p[j]) / 2;
                for (int k = l; k < j; k++) {
                    if (dis(o, p[k]) < r || cmp(dis(o, p[k]), r))
                        continue;
                    o = geto(p[i], p[j], p[k]);
                    r = dis(o, p[i]);
                }
            }
            s[l][i] = r;
        }
    }
//    for(int i = 1; i <= n; i++)
//    	f[0][i] = 1E18;
//    for(int i = 1; i <= k; i++)
//    	for(int j = 1; j <= n; j++) {
//    		f[i][j] = 1E18;
//    		for(int t = 0; t < j; t++)
//    			f[i][j] = min(f[i][j], f[i - 1][t] + s[t + 1][j]);
//		}
//	printf("%.10lf\n", f[k][n]);
    for(int i = 1; i <= n; i++)
    	for(int j = i; j >= 1; j--)
    		if(j == 1 || !cmp(s[j - 1][i], s[j][i]))
				v[i].push_back(j);
	printf("%.10lf\n", F(k, n));
    return 0;
}