#define MOD_TYPE 1 #pragma region Macros #include using namespace std; #if 0 #include #include using Int = boost::multiprecision::cpp_int; using lld = boost::multiprecision::cpp_dec_float_100; #endif #if 1 #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #endif using ll = long long int; using ld = long double; using pii = pair; using pll = pair; using pld = pair; template using smaller_queue = priority_queue, greater>; constexpr ll MOD = (MOD_TYPE == 1 ? (ll)(1e9 + 7) : 998244353); constexpr int INF = (int)1e9 + 10; constexpr ll LINF = (ll)4e18; constexpr ld PI = acos(-1.0); constexpr ld EPS = 1e-9; constexpr int Dx[] = {0, 0, -1, 1, -1, 1, -1, 1, 0}; constexpr int Dy[] = {1, -1, 0, 0, -1, -1, 1, 1, 0}; #define REP(i, m, n) for (ll i = m; i < (ll)(n); ++i) #define rep(i, n) REP(i, 0, n) #define REPI(i, m, n) for (int i = m; i < (int)(n); ++i) #define repi(i, n) REPI(i, 0, n) #define MP make_pair #define MT make_tuple #define YES(n) cout << ((n) ? "YES" : "NO") << "\n" #define Yes(n) cout << ((n) ? "Yes" : "No") << "\n" #define possible(n) cout << ((n) ? "possible" : "impossible") << "\n" #define Possible(n) cout << ((n) ? "Possible" : "Impossible") << "\n" #define all(v) v.begin(), v.end() #define NP(v) next_permutation(all(v)) #define dbg(x) cerr << #x << ":" << x << "\n"; struct io_init { io_init() { cin.tie(0); ios::sync_with_stdio(false); cout << setprecision(30) << setiosflags(ios::fixed); }; } io_init; template inline bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; } inline ll CEIL(ll a, ll b) { return (a + b - 1) / b; } template inline void Fill(A (&array)[N], const T &val) { fill((T *)array, (T *)(array + N), val); } template constexpr istream &operator>>(istream &is, pair &p) noexcept { is >> p.first >> p.second; return is; } template constexpr ostream &operator<<(ostream &os, pair &p) noexcept { os << p.first << " " << p.second; return os; } #pragma endregion // -------------------------------------- struct UnionFind { public: UnionFind() : _n(0) {} UnionFind(int n) : _n(n), parent_or_size(n, -1) {} int unite(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = root(a), y = root(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return root(a) == root(b); } int root(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = root(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[root(a)]; } vector> groups() { vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = root(i); group_size[leader_buf[i]]++; } vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( remove_if(result.begin(), result.end(), [&](const vector &v) { return v.empty(); }), result.end()); return result; } private: int _n; vector parent_or_size; }; // 01BFS template struct BFS { vector d; vector>> E; BFS(int V, T INF) : d(V, INF), E(V) {} void add_edge(int u, int v, bool c, bool directed = true) { E[u].push_back({v, c}); if (!directed) E[v].push_back({u, c}); } void calc(int s) { d[s] = T(0); deque que; que.push_front(s); while (!que.empty()) { int u = que.front(); que.pop_front(); for (auto [v, c] : E[u]) { if (d[v] <= d[u] + c) continue; d[v] = d[u] + c; if (!c) que.push_front(v); else que.push_back(v); } } } }; void solve() { int n, m; cin >> n >> m; vector s(m), t(m), d(m); rep(i, m) { cin >> s[i] >> t[i] >> d[i]; s[i]--, t[i]--; } auto simulate = [&](ll x) { UnionFind uf(n); rep(i, m) { if (d[i] >= x) uf.unite(s[i], t[i]); } return uf.same(0, n - 1); }; auto binary_search = [&]() { int lo = 0, hi = 1e9 + 10; while (hi - lo > 1) { int mi = (lo + hi) / 2; if (simulate(mi)) lo = mi; else hi = mi; } return lo; }; int W = binary_search(); BFS bfs(n, INF); rep(i, m) { if (d[i] >= W) bfs.add_edge(s[i], t[i], 1, false); } bfs.calc(0); cout << W << " " << bfs.d[n - 1] << "\n"; } int main() { solve(); }