// A + B + C = Opt のもとで A, B, C を乱択で探す。 // ジャッジコードのテスト用 #include using i64 = long long; int main() { auto start = std::chrono::system_clock::now(); int n, m; scanf("%d%d", &n, &m); std::vector u(m), v(m), a(n), b(n), c(n); std::vector> g(n); for(int i = 0; i < m; i++) { scanf("%d%d", &u[i], &v[i]); u[i]--; v[i]--; g[u[i]].push_back(v[i]); g[v[i]].push_back(u[i]); } for(int i = 0; i < n; i++) scanf("%d%d%d", &a[i], &b[i], &c[i]); if(n == 1) { // no case exist } std::vector d(n); for(int i = 0; i < n; i++) d[i] = (i64)a[i] + b[i] + c[i]; for(int i = 0; i < n; i++) { int min = std::min({a[i], b[i], c[i]}); int max = std::max({a[i], b[i], c[i]}); a[i] = min; b[i] = d[i] - min - max; c[i] = max; } int min_v = g[0][0]; for(auto v: g[0]) { if(d[v] < d[min_v]) min_v = v; } auto f = [&](i64 A, i64 B = 1, i64 C = 1) -> bool { if(d[0] >= A + B + C) return false; i64 min = std::min({A, B, C}); i64 max = std::max({A, B, C}); B = A + B + C - min - max; A = min; C = max; // A <= B <= C auto update = [&](int x) { if(C < x) { A = B; B = C; C = x; } else if(B < x) { A = B; B = x; } else if(A < x) { A = x; } }; update(c[0]); if(d[min_v] >= A + B + C) return false; using P = std::pair; std::priority_queue, std::greater<>> qu; qu.push({d[0], 0}); std::vector used(n); used[0] = true; while(!qu.empty()) { auto [sum, v] = qu.top(); qu.pop(); if(sum >= A + B + C) return false; if(v == n - 1) return true; update(a[v]); update(b[v]); update(c[v]); for(int to: g[v]) { if(used[to]) continue; used[to] = true; qu.push({d[to], to}); } } return false; }; i64 ng = 1, ok = 3'000'000'000LL; while(ok - ng > 1) { i64 mid = ng + (ok - ng) / 2; if(f(mid)) ok = mid; else ng = mid; } std::random_device seed; std::mt19937 engine(seed()); auto get_random = [&](i64 x) { std::uniform_int_distribution dist(0, x); return dist(engine); }; i64 sum = ok - 1; while(true) { auto now = std::chrono::system_clock::now(); if(std::chrono::duration_cast(now - start).count() > 4000) break; i64 A = get_random(sum); i64 B = get_random(sum - A); i64 C = sum - A - B; A++; B++; C++; assert(A + B + C == ok + 2); if(!f(A, B, C)) continue; printf("%lld %lld %lld\n", A, B, C); return 0; } std::abort(); return 0; }