#include<bits/stdc++.h>
using std::cin;
using std::cout;
const int N = 2005;

const int mod = (1u << 31) - 1;
const int base = 233811181;
using db = long double;
using u64 = unsigned long long;
int n, k;
int x[N], y[N];
struct vec2 {
	db x, y;
	db norm() const { return x * x + y * y; }
	db abs() const { return sqrt(norm()); }
} a[N];
vec2 operator + (vec2 x, vec2 y) { return {x.x + y.x, x.y + y.y}; }
vec2 operator - (vec2 x, vec2 y) { return {x.x - y.x, x.y - y.y}; }
vec2 operator * (vec2 x, db y) { return {x.x * y, x.y * y}; }
vec2 operator / (vec2 x, db y) { return {x.x / y, x.y / y}; }
vec2 r90(vec2 x) { return {-x.y, x.x}; }
db operator * (vec2 x, vec2 y) { return x.x * y.y - x.y * y.x; }


struct line : vec2 {
	db z;
	line(db a, db b, db c) : vec2{a, b}, z(c) {}
	line (vec2 a, vec2 b) : vec2(r90(b - a)), z(a * b) {}
	db operator () (vec2 o) const { return x * o.x + y * o.y + z; }
	line perp() const { return {y, -x, 0}; }
	line para(vec2 o) const { return {x, y, z - (*this)(o)}; }
};

vec2 operator & (line x, line y) {
	return vec2{vec2{x.z, x.y} * vec2{y.z, y.y}, vec2{x.x, x.z} * vec2{y.x, y.z}} / -(vec2(x) * vec2(y));
}

const db eps = 1e-8;
struct ball {
	vec2 o; db r;
	db in(vec2 x) {
		return (x - o).abs() <= r + eps;
	}
};
ball getball(vec2 x, vec2 y, vec2 z) {
	db a = (x - y).norm();
	db b = (x - z).norm();
	db c = (y - z).norm();
	if(a >= b + c) return {(x + y) / 2, sqrt(a) / 2};
	if(b >= a + c) return {(x + z) / 2, sqrt(b) / 2};
	if(c >= b + a) return {(z + y) / 2, sqrt(c) / 2};
	line A = line(x, y).perp().para((x + y) / 2);
	line B = line(z, y).perp().para((z + y) / 2);
	vec2 o = A & B;
	return {o, (x - o).abs()};
}

ball pb[N][N];
db dp[N][N];

int main() {
	std::ios::sync_with_stdio(false), cin.tie(0);
	cin >> n >> k >> x[1];
	y[1] = ((u64) x[1] * base + 1) % mod;
	for(int i = 2;i <= n;++i) {
		x[i] = ((u64) y[i - 1] * base + 1) % mod;
		y[i] = ((u64) x[i] * base + 1) % mod;
	}
	for(int i = 1;i <= n;++i) a[i] = {x[i], y[i]};
	for(int i = 1;i <= n;++i)
		for(int j = 0;j <= n;++j)
			dp[i][j] = 1e18;
	for(int i = 1;i <= n;++i) {
		pb[i][i] = {a[i], 0};
	}
	for(int i = n;i >= 1;--i) {
		for(int j = i + 1;j <= n;++j) {
			if(pb[i][j - 1].in(a[j])) {
				pb[i][j] = pb[i][j - 1];
				continue;
			}
			if(pb[i + 1][j].in(a[i])) {
				pb[i][j] = pb[i + 1][j];
				continue;
			}
			pb[i][j] = {(a[i] + a[j]) / 2, (a[i] - a[j]).abs() / 2};
			for(int k = i + 1;k < j;++k) {
				ball t = getball(a[i], a[j], a[k]);
				if(t.r > pb[i][j].r) pb[i][j] = t;
			}
		}
	}
	for(int i = 1;i <= n;++i) {
		for(int j = i;j <= n;++j) {
			if(j == n || pb[i][j].r + eps < pb[i][j + 1].r) {
				for(int l = 1;l <= k;++l) {
					dp[j][l] = std::min(dp[j][l], dp[i - 1][l - 1] + pb[i][j].r);
				}
			}
		}
	}
	db ans = 1e18;
	for(int i = k;i >= 1;--i) ans = std::min(ans, dp[n][i]);
	printf("%.10Lf\n", ans);
}