This documentation is automatically generated by online-judge-tools/verification-helper
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2950
// verification-helper: ERROR 1e-4
#include <random>
#include <chrono>
namespace lib {
using namespace std;
// Rolling Hash {{{
struct RollingHash {
static const uint64_t mod = (1ull << 61ull) - 1;
using uint128_t = __uint128_t;
const uint64_t base;
vector< uint64_t > power;
static inline uint64_t add(uint64_t a, uint64_t b) {
if((a += b) >= mod) a -= mod;
return a;
}
static inline uint64_t mul(uint64_t a, uint64_t b) {
uint128_t c = (uint128_t) a * b;
return add(c >> 61, c & mod);
}
static inline uint64_t generate_base() {
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
uniform_int_distribution< uint64_t > rand(1, RollingHash::mod - 1);
return rand(mt);
}
inline void expand(size_t sz) {
if(power.size() < sz + 1) {
int pre_sz = (int) power.size();
power.resize(sz + 1);
for(int i = pre_sz - 1; i < (int)sz; i++) {
power[i + 1] = mul(power[i], base);
}
}
}
explicit RollingHash(uint64_t base = generate_base()) : base(base), power{1} {}
vector< uint64_t > build(const string &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
template< typename T >
vector< uint64_t > build(const vector< T > &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
uint64_t query(const vector< uint64_t > &s, int l, int r) {
expand(r - l);
return add(s[r], mod - mul(s[l], power[r - l]));
}
uint64_t combine(uint64_t h1, uint64_t h2, size_t h2len) {
expand(h2len);
return add(mul(h1, power[h2len]), h2);
}
int lcp(const vector< uint64_t > &a, int l1, int r1, const vector< uint64_t > &b, int l2, int r2) {
int len = min(r1 - l1, r2 - l2);
int low = 0, high = len + 1;
while(high - low > 1) {
int mid = (low + high) / 2;
if(query(a, l1, l1 + mid) == query(b, l2, l2 + mid)) low = mid;
else high = mid;
}
return low;
}
};
// }}}
}
#include "src/real-geometry/position/point-polygon-positional-relationships.hpp"
#include "src/real-geometry/point-cloud/convex-hull-with-index.hpp"
#include "src/real-geometry/position/intersect-ss.hpp"
#include "src/real-geometry/operation/cross-product.hpp"
#include "src/real-geometry/utility/sign.hpp"
#include <iostream>
#include <complex>
#include <set>
#include <unordered_set>
#include <queue>
#include <utility>
#include <vector>
#include <functional>
template< typename T >
using vector = std::vector<T>;
void solve(int n, int k) {
lib::RollingHash roll;
using u64 = long long;
using std::pair;
using R = long double;
using points = geometry::points<R>;
using polygon = geometry::polygon<R>;
using segment = geometry::segment<R>;
points pts(n);
for (auto &pt : pts) std::cin >> pt;
std::unordered_set< u64 > used;
using T = pair<double, int>;
std::priority_queue< T, vector<T>, std::greater<T> > pq;
// TODO: #37
auto calc_perimeter = [&](const vector< int > &vs) {
using std::abs;
double len = abs(pts[vs.front()] - pts[vs.back()]);
for (int i = 1; i < (int)vs.size(); i++) {
len += abs(pts[vs[i]] - pts[vs[i - 1]]);
}
return len;
};
auto calc_hash = [&](const vector< int > &vs) {
auto rh = roll.build(vs);
return roll.query(rh, 0, vs.size());
};
auto insert_ptsi = [&](vector< int > vs, int i, int j) {
vs.insert(vs.begin() + j + 1, i);
return vs;
};
vector< vector<int> > vss;
{
auto ds = geometry::convex_hull_with_index(pts);
vector< int > vs;
for (auto &v : ds.second) vs.emplace_back(v);
u64 hash = calc_hash(vs);
double len = calc_perimeter(vs);
pq.emplace(len, vss.size());
vss.emplace_back(vs);
used.emplace(hash);
}
for (int qi = 1; qi < k and not pq.empty(); qi++) {
auto [d, idx] = pq.top();
pq.pop();
auto as = vss[idx];
int m = as.size();
std::set< int > st(as.begin(), as.end());
for (int i = 0; i < n; i++) {
if (st.count(i)) continue;
for (int j = 0; j < m; j++) {
auto vs = insert_ptsi(as, i, j);
u64 hash = calc_hash(vs);
if (used.count(hash)) {
continue;
}
used.emplace(hash);
// TODO: #35
segment s1(pts[i], pts[as[j]]);
segment s2(pts[i], pts[as[(j + 1) % m]]);
int cnt = 0;
for (int k = 0; k < m; k++) {
segment s(pts[as[k]], pts[as[(k + 1) % m]]);
if (intersect_ss(s, s1)) cnt++;
if (intersect_ss(s, s2)) cnt++;
}
if (cnt != 4) continue;
polygon poly;
bool f = false;
for (auto i : vs) poly.emplace_back(pts[i]);
for (auto &p : pts) if (point_polygon_positional_relationships(p, poly) == 0) f = true;
if (f) continue;
double len = calc_perimeter(vs);
pq.emplace(len, vss.size());
vss.emplace_back(vs);
}
}
}
if (pq.empty()) {
std::cout << -1 << std::endl;
return;
}
std::cout << pq.top().first << std::endl;
}
signed main() {
int n, k;
while (std::cin >> n >> k, n) {
solve(n, k);
}
}
#line 1 "test/aoj/icpc/2950.test.cpp"
// verification-helper: PROBLEM https://onlinejudge.u-aizu.ac.jp/problems/2950
// verification-helper: ERROR 1e-4
#include <random>
#include <chrono>
namespace lib {
using namespace std;
// Rolling Hash {{{
struct RollingHash {
static const uint64_t mod = (1ull << 61ull) - 1;
using uint128_t = __uint128_t;
const uint64_t base;
vector< uint64_t > power;
static inline uint64_t add(uint64_t a, uint64_t b) {
if((a += b) >= mod) a -= mod;
return a;
}
static inline uint64_t mul(uint64_t a, uint64_t b) {
uint128_t c = (uint128_t) a * b;
return add(c >> 61, c & mod);
}
static inline uint64_t generate_base() {
mt19937_64 mt(chrono::steady_clock::now().time_since_epoch().count());
uniform_int_distribution< uint64_t > rand(1, RollingHash::mod - 1);
return rand(mt);
}
inline void expand(size_t sz) {
if(power.size() < sz + 1) {
int pre_sz = (int) power.size();
power.resize(sz + 1);
for(int i = pre_sz - 1; i < (int)sz; i++) {
power[i + 1] = mul(power[i], base);
}
}
}
explicit RollingHash(uint64_t base = generate_base()) : base(base), power{1} {}
vector< uint64_t > build(const string &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
template< typename T >
vector< uint64_t > build(const vector< T > &s) const {
int sz = s.size();
vector< uint64_t > hashed(sz + 1);
for(int i = 0; i < sz; i++) {
hashed[i + 1] = add(mul(hashed[i], base), s[i]);
}
return hashed;
}
uint64_t query(const vector< uint64_t > &s, int l, int r) {
expand(r - l);
return add(s[r], mod - mul(s[l], power[r - l]));
}
uint64_t combine(uint64_t h1, uint64_t h2, size_t h2len) {
expand(h2len);
return add(mul(h1, power[h2len]), h2);
}
int lcp(const vector< uint64_t > &a, int l1, int r1, const vector< uint64_t > &b, int l2, int r2) {
int len = min(r1 - l1, r2 - l2);
int low = 0, high = len + 1;
while(high - low > 1) {
int mid = (low + high) / 2;
if(query(a, l1, l1 + mid) == query(b, l2, l2 + mid)) low = mid;
else high = mid;
}
return low;
}
};
// }}}
}
#line 2 "src/real-geometry/position/point-polygon-positional-relationships.hpp"
#line 2 "src/real-geometry/class/point.hpp"
#line 2 "src/real-geometry/class/vector.hpp"
#include <complex>
#include <iostream>
namespace geometry {
template< typename R >
class vec2d : public std::complex< R > {
using complex = std::complex< R >;
public:
using complex::complex;
vec2d(const complex &c): complex::complex(c) {}
const R x() const { return this->real(); }
const R y() const { return this->imag(); }
friend vec2d operator*(const vec2d &v, const R &k) {
return vec2d(v.x() * k, v.y() * k);
}
friend vec2d operator*(const R &k, const vec2d &v) {
return vec2d(v.x() * k, v.y() * k);
}
friend std::istream &operator>>(std::istream &is, vec2d &v) {
R x, y;
is >> x >> y;
v = vec2d(x, y);
return is;
}
};
}
#line 4 "src/real-geometry/class/point.hpp"
#include <vector>
namespace geometry {
template< typename R >
using point = vec2d<R>;
template< typename R >
using points = std::vector< point< R > >;
}
#line 2 "src/real-geometry/class/polygon.hpp"
#line 4 "src/real-geometry/class/polygon.hpp"
#line 6 "src/real-geometry/class/polygon.hpp"
namespace geometry {
template< typename R >
using polygon = std::vector< point<R> >;
template< typename R >
using polygons = std::vector< polygon<R> >;
}
#line 2 "src/real-geometry/numbers/posision-of-point-polygon.hpp"
namespace geometry::number::point_polygon_positional_relationships {
constexpr int OUT = 0;
constexpr int ON_EDGE = 1;
constexpr int IN = 2;
}
#line 2 "src/real-geometry/operation/cross-product.hpp"
#line 4 "src/real-geometry/operation/cross-product.hpp"
namespace geometry {
template< typename R >
R cross_product(const vec2d<R> &a, const vec2d<R> &b) {
return a.x() * b.y() - a.y() * b.x();
}
}
#line 2 "src/real-geometry/operation/inner-product.hpp"
#line 4 "src/real-geometry/operation/inner-product.hpp"
namespace geometry {
template< typename R >
R inner_product(const vec2d<R> &a, const vec2d<R> &b) {
return a.x() * b.x() + a.y() * b.y();
}
}
#line 2 "src/real-geometry/common/size-alias.hpp"
#include <cstddef>
namespace geometry {
using isize = std::ptrdiff_t;
using usize = std::size_t;
}
#line 2 "src/real-geometry/utility/next-idx.hpp"
#line 4 "src/real-geometry/utility/next-idx.hpp"
namespace geometry {
inline usize next_idx(usize idx, usize size) {
return idx + 1 == size ? 0 : idx + 1;
}
}
#line 2 "src/real-geometry/utility/sign.hpp"
#line 2 "src/real-geometry/common/const/eps.hpp"
#line 2 "src/real-geometry/common/float-alias.hpp"
namespace geometry {
using f80 = long double;
using f64 = double;
}
#line 4 "src/real-geometry/common/const/eps.hpp"
namespace geometry {
inline static f80 &eps() {
static f80 EPS = 1e-10;
return EPS;
}
void set_eps(f80 EPS) {
eps() = EPS;
}
}
#line 2 "src/real-geometry/numbers/sign.hpp"
#line 2 "src/real-geometry/common/int-alias.hpp"
namespace geometry {
using i32 = int;
using i64 = long long;
}
#line 4 "src/real-geometry/numbers/sign.hpp"
namespace geometry::number::sign {
constexpr i32 PLUS = +1;
constexpr i32 ZERO = 0;
constexpr i32 MINUS = -1;
}
#line 5 "src/real-geometry/utility/sign.hpp"
namespace geometry {
using namespace geometry::number::sign;
template< typename R >
inline int sign(R r) {
if (r < -eps()) return MINUS;
if (r > +eps()) return PLUS;
return ZERO;
}
}
#line 11 "src/real-geometry/position/point-polygon-positional-relationships.hpp"
#include <algorithm>
namespace geometry {
// O(N)
template< typename R >
int point_polygon_positional_relationships(const point<R> &p, const polygon<R> &poly) {
using namespace number::point_polygon_positional_relationships;
usize n = poly.size();
bool in = false;
for (usize i = 0; i < n; i++) {
usize j = next_idx(i, n);
point<R> a = poly[i] - p, b = poly[j] - p;
if (a.y() > b.y()) std::swap(a, b);
if (a.y() <= 0 and 0 < b.y() and cross_product(a, b) < 0) {
in = not in;
}
if (sign(cross_product(a, b)) == 0 and sign(inner_product(a, b)) <= 0) {
return ON_EDGE;
}
}
return in ? IN : OUT;
}
}
#line 2 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"
#line 2 "src/real-geometry/compare/compare-x.hpp"
#line 2 "src/real-geometry/utility/equals/real-number.hpp"
#line 4 "src/real-geometry/utility/equals/real-number.hpp"
namespace geometry {
template< typename R >
bool equals(R a, R b) {
return sign(a - b) == 0;
}
}
#line 5 "src/real-geometry/compare/compare-x.hpp"
namespace geometry {
template< typename R >
bool compare_x(const point<R> &a, const point<R> &b) {
return not equals(a.x(), b.x()) ? a.x() < b.x() : a.y() < b.y();
}
}
#line 8 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"
#line 10 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"
#include <numeric>
#include <tuple>
#include <utility>
#line 14 "src/real-geometry/point-cloud/convex-hull-with-index.hpp"
namespace geometry {
template< typename R >
std::pair< polygon<R>, std::vector< usize > > convex_hull_with_index(const points<R> &pts) {
usize n = pts.size();
if (n <= 2) {
std::vector< usize > idxs(n);
std::iota(idxs.begin(), idxs.end(), 0);
return {pts, idxs};
}
std::vector< std::pair< point<R>, usize > > ps;
ps.reserve(n);
for (usize i = 0; i < n; i++) {
ps.emplace_back(pts[i], i);
}
auto cmp = [](const std::pair<point<R>, usize> &a, const std::pair<point<R>, usize> &b) {
return compare_x(a.first, b.first);
};
std::sort(ps.begin(), ps.end(), cmp);
std::vector< usize > idxs(2 * n);
polygon<R> poly(2 * n);
usize k = 0, i = 0;
auto check = [&](usize i) {
return sign(cross_product<R>(poly[k - 1] - poly[k - 2], ps[i].first - poly[k - 1])) == -1;
};
while (i < n) {
while (k >= 2 and check(i)) k--;
std::tie(poly[k], idxs[k]) = ps[i];
k++; i++;
}
i = n - 2;
usize t = k + 1;
while (true) {
while (k >= t and check(i)) k--;
std::tie(poly[k], idxs[k]) = ps[i];
k++;
if (not i) break;
i--;
}
poly.resize(k - 1);
idxs.resize(k - 1);
return {poly, idxs};
}
}
#line 2 "src/real-geometry/position/intersect-ss.hpp"
#line 2 "src/real-geometry/class/segment.hpp"
#line 2 "src/real-geometry/utility/equals/vector.hpp"
#line 5 "src/real-geometry/utility/equals/vector.hpp"
namespace geometry {
template< typename R >
bool equals(const vec2d<R> &a, const vec2d<R> &b) {
return equals(a.x(), b.x()) and equals(a.y(), b.y());
}
}
#line 5 "src/real-geometry/class/segment.hpp"
#include <cassert>
#line 8 "src/real-geometry/class/segment.hpp"
namespace geometry {
template< typename R >
class segment {
public:
point<R> a, b;
segment() = default;
segment(point<R> a, point<R> b) : a(a), b(b) {
assert(not equals(a, b));
}
};
template< typename R >
using segments = std::vector< segment<R> >;
}
#line 2 "src/real-geometry/operation/ccw.hpp"
#line 2 "src/real-geometry/numbers/ccw.hpp"
namespace geometry::number::ccw {
constexpr int COUNTER_CLOCKWISE = +1;
constexpr int CLOCKWISE = -1;
constexpr int ONLINE_BACK = +2; // c-a-b
constexpr int ONLINE_FRONT = -2; // a-b-c
constexpr int ON_SEGMENT = 0; // a-c-b
}
#line 8 "src/real-geometry/operation/ccw.hpp"
namespace geometry {
using namespace geometry::number::ccw;
template< typename R >
int ccw(const point<R> &a, point<R> b, point<R> c) {
b = b - a, c = c - a;
if (sign(cross_product(b, c)) == +1) return COUNTER_CLOCKWISE;
if (sign(cross_product(b, c)) == -1) return CLOCKWISE;
if (sign(inner_product(b, c)) == -1) return ONLINE_BACK;
if (std::norm(b) < std::norm(c)) return ONLINE_FRONT;
return ON_SEGMENT;
}
}
#line 5 "src/real-geometry/position/intersect-ss.hpp"
namespace geometry {
template< typename R >
bool intersect_ss(const segment<R> &s1, const segment<R> &s2) {
return ccw(s1.a, s1.b, s2.a) * ccw(s1.a, s1.b, s2.b) <= 0 and
ccw(s2.a, s2.b, s1.a) * ccw(s2.a, s2.b, s1.b) <= 0;
}
}
#line 91 "test/aoj/icpc/2950.test.cpp"
#line 94 "test/aoj/icpc/2950.test.cpp"
#include <set>
#include <unordered_set>
#include <queue>
#line 99 "test/aoj/icpc/2950.test.cpp"
#include <functional>
template< typename T >
using vector = std::vector<T>;
void solve(int n, int k) {
lib::RollingHash roll;
using u64 = long long;
using std::pair;
using R = long double;
using points = geometry::points<R>;
using polygon = geometry::polygon<R>;
using segment = geometry::segment<R>;
points pts(n);
for (auto &pt : pts) std::cin >> pt;
std::unordered_set< u64 > used;
using T = pair<double, int>;
std::priority_queue< T, vector<T>, std::greater<T> > pq;
// TODO: #37
auto calc_perimeter = [&](const vector< int > &vs) {
using std::abs;
double len = abs(pts[vs.front()] - pts[vs.back()]);
for (int i = 1; i < (int)vs.size(); i++) {
len += abs(pts[vs[i]] - pts[vs[i - 1]]);
}
return len;
};
auto calc_hash = [&](const vector< int > &vs) {
auto rh = roll.build(vs);
return roll.query(rh, 0, vs.size());
};
auto insert_ptsi = [&](vector< int > vs, int i, int j) {
vs.insert(vs.begin() + j + 1, i);
return vs;
};
vector< vector<int> > vss;
{
auto ds = geometry::convex_hull_with_index(pts);
vector< int > vs;
for (auto &v : ds.second) vs.emplace_back(v);
u64 hash = calc_hash(vs);
double len = calc_perimeter(vs);
pq.emplace(len, vss.size());
vss.emplace_back(vs);
used.emplace(hash);
}
for (int qi = 1; qi < k and not pq.empty(); qi++) {
auto [d, idx] = pq.top();
pq.pop();
auto as = vss[idx];
int m = as.size();
std::set< int > st(as.begin(), as.end());
for (int i = 0; i < n; i++) {
if (st.count(i)) continue;
for (int j = 0; j < m; j++) {
auto vs = insert_ptsi(as, i, j);
u64 hash = calc_hash(vs);
if (used.count(hash)) {
continue;
}
used.emplace(hash);
// TODO: #35
segment s1(pts[i], pts[as[j]]);
segment s2(pts[i], pts[as[(j + 1) % m]]);
int cnt = 0;
for (int k = 0; k < m; k++) {
segment s(pts[as[k]], pts[as[(k + 1) % m]]);
if (intersect_ss(s, s1)) cnt++;
if (intersect_ss(s, s2)) cnt++;
}
if (cnt != 4) continue;
polygon poly;
bool f = false;
for (auto i : vs) poly.emplace_back(pts[i]);
for (auto &p : pts) if (point_polygon_positional_relationships(p, poly) == 0) f = true;
if (f) continue;
double len = calc_perimeter(vs);
pq.emplace(len, vss.size());
vss.emplace_back(vs);
}
}
}
if (pq.empty()) {
std::cout << -1 << std::endl;
return;
}
std::cout << pq.top().first << std::endl;
}
signed main() {
int n, k;
while (std::cin >> n >> k, n) {
solve(n, k);
}
}