#include <bits/stdc++.h>
using namespace std;
#define int long long
#define MOD ((1ll << 31) - 1)
int X[2010], Y[2010];
long double p[2010][2010];
long double dis[2010][2010];
long double get_dis(int x1, int y1, int x2, int y2) {
    long double ret = sqrt(1ll * (x1 - x2) * (x1 - x2) + 1ll * (y1 - y2) * (y1 - y2));
    return ret;
}
long double f[2010][2010];

#define fst first
#define snd second
#define pb push_back
typedef pair<long double, long double> pii;
const long double eps = 1e-8;
const long double pi = acos(-1.0);
inline pii operator+(const pii &x, const pii &y) {
	return {x.fst + y.fst, x.snd + y.snd};
}
inline pii operator-(const pii &x, const pii &y) {
	return {x.fst - y.fst, x.snd - y.snd};
}
long double len(const pii &x) {
	return sqrt(x.fst * x.fst + x.snd * x.snd);
}
pii dir(const pii &x) {
	return (pii){x.fst / len(x), x.snd / len(x)};
}
long double angle(const pii &x) {
	pii y = dir(x);
	if(x.snd >= 0) return acos(y.fst);
	return 2 * pi - acos(y.fst);
}

pii a[2010];
struct P {
    long double x, y, r;
};

P calc(int lb, int rb) {
    int u = lb;
    for(int i = lb; i <= rb; i++) a[i] = {X[i], Y[i]};
	vector<long double> ad, rm;
	long double l = 0, r = INT_MAX, mid;
    pii cen, tmp;
	for(; r - l > eps;) {
		mid = (l + r) / 2;
		int cnt = 1, flag = 0;
		ad.clear(), rm.clear();
		for(int i = lb; i <= rb; i++) {
			if(i == u) continue;
			long double le = len(a[i] - a[u]), r1 = mid, r2 = mid;
			if(le + r1 <= r2) {
                assert(0);
			}
			if(le + r2 < r1 || r1 + r2 < le) continue;
			long double theta = angle(a[i] - a[u]), delta, tx, ty;
			delta = acos((r1 * r1 + le * le - r2 * r2) / 2 / r1 / le);
			tx = theta - delta, ty = theta + delta;
			for(; tx < 0; tx += 2 * pi, ty += 2 * pi);
			if(ty <= 2 * pi) {
				ad.pb(tx), rm.pb(ty);
			}
			else {
				ad.pb(tx), rm.pb(2 * pi), ad.pb(0), rm.pb(ty - 2 * pi);
			}
		}
		sort(ad.begin(), ad.end()), sort(rm.begin(), rm.end());
		for(auto it1 = ad.begin(), it2 = rm.begin(); it1 != ad.end() || it2 != rm.end();) {
			if(it1 != ad.end() && (it2 == rm.end() || *it1 < *it2)) {
                tmp = a[u] + (pii){cos(*it1) * mid, sin(*it1) * mid};
				++cnt, ++it1;
			}
			else --cnt, ++it2;
			if(cnt >= rb - lb + 1) {
				flag = 1; break;
			}
		}
		if(flag) cen = tmp, r = mid;
		else l = mid;
	}
    return (P){cen.fst, cen.snd, r};
}
vector<pair<int, long double>> from[2010];
signed main() {
	ios::sync_with_stdio(0);
    cin.tie(0), cout.tie(0);
	int n, K;
    cin >> n >> K >> X[1];
    for(int i = 1; i <= n; ++ i) {
        if(i > 1) {
            X[i] = ((Y[i - 1] * 233811181ll) + 1) % MOD;
        }
        Y[i] = ((X[i] * 233811181ll) + 1) % MOD;
    }
    for(int i = 1; i <= n; ++ i) {
        for(int j = i; j <= n; ++ j) {
            dis[i][j] = dis[j][i] = get_dis(X[i], Y[i], X[j], Y[j]);
        }
    }
    for(int i = 1; i <= n; ++ i) {
        P now = calc(i - 1, i);
        p[i - 1][i] = now.r;
        from[i].push_back({i - 1, 0});
        from[i].push_back({i - 2, p[i - 1][i]});
        for(int j = i - 2; j >= 1; -- j)  {
            if(now.r * now.r >= (X[j] - now.x) * (X[j] - now.x) + (Y[j] - now.y) * (Y[j] - now.y)) {
                p[j][i] = p[j + 1][i];
                from[i][from[i].size() - 1].first = j - 1;
            }
            else {
                now = calc(j, i);
                p[j][i] = now.r;
                from[i].push_back({j - 1, p[j][i]});
            }
            // p[i][j] = p[i][j - 1];
            // for(int k = i; k <= j - 1; ++ k) {
            //     p[i][j] = max(p[i][j], dis[k][j]);
            // } 
            // cerr << i << " " << j << " " << p[i][j] << endl;
        }

    }
    if(K <= 50) {
        for(int i = 0; i <= n; ++ i) {
            for(int j = 0; j <= n; ++ j) {
                f[i][j] = 1e18;
            }
        }
        f[0][0] = 0;
        for(int i = 1; i <= n; ++ i) {
            for(int j = 1; j <= K && j <= i; ++ j) {
                // f[i][j] = 1e15;
                for(auto [k, pp] : from[i]) {
                    f[i][j] = min(f[i][j], f[k][j - 1] + pp);
                }
                f[i][j] = min(f[i][j], f[j - 1][j - 1] + p[j][i]); 
                // for(int k = 0ll; k <= i - 1; ++ k) {
                //     // if(i == 1 && j == 1) {
                //     //     cerr << p[k + 1][i] << endl;
                //     // }
                //     f[i][j] = min(f[i][j], f[k][j - 1] + p[k + 1][i]);
                // }
                // if(i <= 20) cerr << i << " " << j << " " << f[i][j] << endl;
            }
        }
        cout << fixed << setprecision(20) << f[n][K] << endl;
    }
    else {
        long double mx = 1e18;
        for(int i = 1; i <= n && i + n - K <= n; ++ i) {
            mx = min(mx, p[i][i + n - K]);
        }
        cout << fixed << setprecision(20) << mx << endl;
    }
}