#include <bits/stdc++.h>
using namespace std;

const int N = 2100;
int n, k;
double x[N], y[N];
uint64_t seed;
int gen() {
    int ret = seed;
    seed = (seed * 233811181 + 1) % 0x7fffffff;
    return ret;
}

const double eps = 1e-12;
double len2(double x, double y) {
    return x * x + y * y;
}
struct circ {
    double x0, y0, r2;
    bool check(double x, double y) {
        return len2(x0 - x, y0 - y) <= r2 * (1 + eps);
    }
};

circ outer_circ(int i, int j, int k) {
    double tx[3] = {x[i], x[j], x[k]}, ty[3] = {y[i], y[j], y[k]};
    double a[3][4];
    for (int i = 0; i < 3; i++) {
        a[i][0] = 2 * tx[i];
        a[i][1] = 2 * ty[i];
        a[i][2] = 1;
        a[i][3] = len2(tx[i], ty[i]);
    }
    for (int i = 0; i < 3; i++) {
        int p = i;
        for (int j = i + 1; j < 3; j++) if (abs(a[j][i]) > abs(a[p][i])) p = j;
        swap(a[p], a[i]);
        auto k = 1 / a[i][i];
        for (int j = i; j < 4; j++) a[i][j] *= k;
        for (int j = 0; j < 3; j++) if (j != i) {
            auto t = a[j][i];
            for (int k = i; k < 4; k++) a[j][k] -= a[i][k] * t;
        }
    }
    double x0 = a[0][3], y0 = a[1][3], r2 = a[2][3] + len2(x0, y0);
    return {x0, y0, r2};
}
circ get_circ(int l, int r) {
    circ c = {x[l], y[l], 0};
    for (int i = l + 1; i <= r; i++) {
        if (c.check(x[i], y[i])) continue;
        c = {(x[i] + x[l]) * .5, (y[i] + y[l]) * .5, len2(x[i] - x[l], y[i] - y[l]) * .25};
        for (int j = l + 1; j < i; j++) if (!c.check(x[j], y[j]))
            c = outer_circ(l, j, i);
    }
    return c;
}

struct info {
    int l, r;
    double x;
    int k;
};
vector<info> buc[N];

double dp[2][N];

double st[12][N];

int main() {
    cin.tie(0)->sync_with_stdio(0), cout.tie(0);
    cin >> n >> k >> seed;
    for (int i = 1; i <= n; i++) {
        x[i] = gen();
        y[i] = gen();
    }

    for (int i = n; i >= 1; i--) {
        circ c = {x[i], y[i], 0};
        int r = i;
        for (int j = i - 1; j; j--) {
            if (c.check(x[j], y[j])) continue;
            buc[i].push_back(info{j + 1, r, sqrt(c.r2)});
            c = get_circ(j, i);
            r = j;
        }
        buc[i].push_back(info{1, r, sqrt(c.r2)});

        for (auto &x: buc[i]) {
            x.k = 31 - __builtin_clz(x.r - x.l + 1);
            x.r -= (1 << x.k) - 1;
        }
    }
    for (int i = 0; i <= n; i++) dp[0][i] = dp[1][i] = 1e30;
    dp[0][0] = 0;
    for (int i = 1; i <= k; i++) {
        auto &f = dp[i & 1], &g = dp[1 ^ i & 1];
        for (int j = 1; j <= n; j++) f[j] = 1e30;
        
        for (int i = 0; i <= n; i++) st[0][i] = g[i];
        for (int j = 0; j < 11; j++)
            for (int i = 0; i + (2 << j) <= n; i++)
                st[j + 1][i] = min(st[j][i], st[j][i + (1 << j)]);

        for (int j = 1; j <= n; j++) {
            for (const auto &i: buc[j]) {
                double mn = min(st[i.k][i.l - 1], st[i.k][i.r - 1]);
                //for (int k = i.l; k <= i.r; k++) mn = min(mn, g[k - 1]);
                f[j] = min(f[j], mn + i.x);
            }
        }
    }
    cout << fixed << setprecision(13) << dp[k & 1][n] << "\n";
}