#include <cmath>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <cfloat>
#define eps 1e-9
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 n, k, 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;
}

double dp_before[N], dp_cur[N];

void compute(int l, int r, int optl, int optr) {
  if (l > r) return;
  int mid = (l + r) >> 1;
  pair<double, int> best = {DBL_MAX, -1};
  for (int k = optl; k <= min(mid, optr); k++) {
    best = min(best, {dp_before[k] + s[k + 1][mid], k});
  }
  dp_cur[mid] = best.first;
  int opt = best.second;
  compute(l, mid - 1, optl, opt);
  compute(mid + 1, r, opt, optr);
}

signed main() {
    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];
    }
    double ans = 0;
    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++)
        dp_cur[i] = DBL_MAX;
    int t = T / (n * k);
    while (k--) {
        memcpy(dp_before, dp_cur, sizeof(dp_cur));
        compute(1, n, 0, n - 1);
        for (int i = 1; i <= n; i++)
            for (int d = 1; d <= t && i - d >= 0; d++)
                dp_cur[i] = min(dp_cur[i], dp_before[i - d] + s[i - d + 1][i]);
    }
    printf("%.10lf", dp_cur[n]);
    return 0;
}