#include using namespace std; #define rep(i, n) for(int i=0; i #include //vectorの中身を空白区切りで出力 template void printv(vector v) { for (int i = 0; i < v.size(); i++) { cout << v[i]; if (i < v.size() - 1) { cout << " "; } } cout << endl; } //vectorの中身を改行区切りで出力 template void print1(vector v) { for (auto x : v) { cout << x << endl; } } //二次元配列を出力 template void printvv(vector> vv) { for (vector v : vv) { printv(v); } } //vectorを降順にソート template void rsort(vector& v) { sort(v.begin(), v.end()); reverse(v.begin(), v.end()); } //昇順priority_queueを召喚 template struct rpriority_queue { priority_queue, greater> pq; void push(T x) { pq.push(x); } void pop() { pq.pop(); } T top() { return pq.top(); } size_t size() { return pq.size(); } bool empty() { return pq.empty(); } }; //mod mod下で逆元を算出する //高速a^n計算(mod ver.) ll power(ll a, ll n) { if (n == 0) { return 1; } else if (n % 2 == 0) { ll x = power(a, n / 2); x *= x; x %= mod; return x; } else { ll x = power(a, n - 1); x *= a; x %= mod; return x; } } //フェルマーの小定理を利用 ll modinv(ll p) { return power(p, mod - 2) % mod; } //Mexを求める struct Mex { map mp; set s; Mex(int Max) { for (int i = 0; i <= Max; i++) { s.insert(i); } } int _mex = 0; void Input(int x) { mp[x]++; s.erase(x); if (_mex == x) { _mex = *begin(s); } } void Remove(int x) { if (mp[x] == 0) { cout << "Mex ERROR!: NO VALUE WILL BE REMOVED" << endl; } mp[x]--; if (mp[x] == 0) { s.insert(x); if (*begin(s) == x) { _mex = x; } } } int mex() { return _mex; } }; //条件分岐でYes/Noを出力するタイプのやつ void YN(bool true_or_false) { cout << (true_or_false ? "Yes" : "No") << endl; } //Union-Find struct UnionFind { vector par; UnionFind(int N) : par(N) { for (int i = 0; i < N; i++) { par[i] = -1; } } //root(x):xの根を求める関数 int root(int x) { if (par[x] == -1) { return x; } else { return par[x] = root(par[x]); } } //isSame(x,y):xとyが同じグループならtrueを返す関数 bool isSame(int x, int y) { if (root(x) == root(y)) { return true; } else { return false; } } //Union(x,y):xとyの根をつなげる関数 void Union(int x, int y) { int X = root(x); int Y = root(y); if (X == Y) { return; } if (X < Y) { swap(X, Y); } par[X] = Y; } }; //最大公約数(ユークリッドの互除法) ll gcd(ll a, ll b) { if (b > a) { swap(a, b); } while (a % b != 0) { ll t = a; a = b; b = t % b; } return b; } //最小公倍数(gcdを定義しておく) ll lcm(ll a, ll b) { ll g = gcd(a, b); ll x = (a / g) * b; return x; } struct SegTree { vector tree; vector lazy; int n = 1; SegTree(int N, int H) { while (n < N) { n *= 2; } vector v(n * 2, H + 1); swap(tree, v); vector u(n * 2, 200005); swap(lazy, u); } void update(int val, int l, int r, int u, int t, int now) { if (l >= t || r <= u) { return; } else if (l <= u && r >= t) { lazy[now] = min(lazy[now], val); } else { tree[now] = min(tree[now], val); update(val, l, r, u, (u + t) / 2, now * 2 + 1); update(val, l, r, (u + t) / 2, t, now * 2 + 2); } } void treeup(int now, int val) { if (tree[now] > val) { tree[now] = val; if (now > 0) { treeup((now - 1) / 2, val); } } } int Min(int l, int r, int u, int t, int now) { if (l >= t || r <= u) { return inf; } else if (l <= u && r >= t) { treeup(now, lazy[now]); return tree[now]; } else { treeup(now, lazy[now]); lazy[now * 2 + 1] = min(lazy[now * 2 + 1], lazy[now]); lazy[now * 2 + 2] = min(lazy[now * 2 + 2], lazy[now]); return min(Min(l, r, u, (u + t) / 2, now * 2 + 1), Min(l, r, (u + t) / 2, t, now * 2 + 2)); } } int query(int l, int r) { return Min(l, r, 0, n, 0); } }; int N, K, m=0; vector> group; vector> plot; ld ans = INF; ld dist(vector x, vector y) { ld d = sqrt((x[0] - y[0]) * (x[0] - y[0]) + (x[1] - y[1]) * (x[1] - y[1])); return d; } void calc() { ld score = 0; for (vector g : group) { map> record; rpriority_queue < tuple> pq; record[0][0] = 0; pq.push({ 0,0,0 }); while (!pq.empty()) { tuple tmp = pq.top(); pq.pop(); ld now_score; bitset<15> b; int now; tie(now_score, b, now) = tmp; for (int x : g) { if (!b[x] && now != x) { b[x] = 1; ld d = dist(plot[now], plot[x]); if (!record[b.to_ullong()].count(x) || record[b.to_ullong()][x] > now_score + d) { record[b.to_ullong()][x] = now_score + d; pq.push({ now_score + d, b.to_ullong(), x}); } b[x] = 0; } } } bitset<15> e = 0; for (int x : g) { e[x] = 1; } score += record[e.to_ullong()][0]; } ans = min(ans, score); } void dfs(int i) { if (i <= N) { for (int j = 0; j < group.size(); j++) { if (group[j].size() <= K) { group[j].push_back(i); dfs(i + 1); group[j].pop_back(); } } if (group.size() < m) { group.push_back({ 0, i }); dfs(i + 1); group.pop_back(); } } else { calc(); } } int main() { cin >> N >> K; for (int i = 0; i < N; i += K) { m++; } plot.push_back({ 0,0 }); rep(i, N) { ld x, y; cin >> x >> y; plot.push_back({ x,y }); } dfs(1); cout << setprecision(10) << fixed; cout << ans << endl; }