#include using namespace std; using int64 = long long; const int mod = 1e9 + 7; // const int mod = 998244353; const int64 infll = (1LL << 62) - 1; const int inf = (1 << 30) - 1; struct IoSetup { IoSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(10); cerr << fixed << setprecision(10); } } iosetup; template< typename T1, typename T2 > ostream &operator<<(ostream &os, const pair< T1, T2 > &p) { os << p.first << " " << p.second; return os; } template< typename T1, typename T2 > istream &operator>>(istream &is, pair< T1, T2 > &p) { is >> p.first >> p.second; return is; } template< typename T > ostream &operator<<(ostream &os, const vector< T > &v) { for(int i = 0; i < (int) v.size(); i++) { os << v[i] << (i + 1 != v.size() ? " " : ""); } return os; } template< typename T > istream &operator>>(istream &is, vector< T > &v) { for(T &in : v) is >> in; return is; } template< typename T1, typename T2 > inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); } template< typename T1, typename T2 > inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); } template< typename T = int64 > vector< T > make_v(size_t a) { return vector< T >(a); } template< typename T, typename... Ts > auto make_v(size_t a, Ts... ts) { return vector< decltype(make_v< T >(ts...)) >(a, make_v< T >(ts...)); } template< typename T, typename V > typename enable_if< is_class< T >::value == 0 >::type fill_v(T &t, const V &v) { t = v; } template< typename T, typename V > typename enable_if< is_class< T >::value != 0 >::type fill_v(T &t, const V &v) { for(auto &e : t) fill_v(e, v); } template< typename F > struct FixPoint : F { FixPoint(F &&f) : F(forward< F >(f)) {} template< typename... Args > decltype(auto) operator()(Args &&... args) const { return F::operator()(*this, forward< Args >(args)...); } }; template< typename F > inline decltype(auto) MFP(F &&f) { return FixPoint< F >{forward< F >(f)}; } struct edge { int to, cost, type, idx; }; using Graph = vector< vector< edge > >; /** * @brief Union-Find * @docs docs/union-find.md */ struct UnionFind { vector< int > data; UnionFind() = default; explicit UnionFind(size_t sz) : data(sz, -1) {} bool unite(int x, int y) { x = find(x), y = find(y); if(x == y) return false; if(data[x] > data[y]) swap(x, y); data[x] += data[y]; data[y] = x; return true; } int find(int k) { if(data[k] < 0) return (k); return data[k] = find(data[k]); } int size(int k) { return -data[find(k)]; } bool same(int x, int y) { return find(x) == find(y); } }; struct sssp { vector< int64 > dist; vector< int > parent, depth; }; sssp dijkstra(const Graph &g, int s) { int n = (int) g.size(); vector< int64 > dist(n, infll); vector< int > depth(n), parent(n); using pi = pair< int64, int >; priority_queue< pi, vector< pi >, greater<> > que; que.emplace(0, s); dist[s] = 0; depth[s] = 0; while(not que.empty()) { auto[d, u] = que.top(); que.pop(); if(dist[u] != d) { continue; } for(auto e : g[u]) { int v = e.to; int64 d2 = d + e.cost; if(dist[v] > d2) { dist[v] = d2; depth[v] = depth[u] + 1; parent[v] = u; que.emplace(d2, v); } } } return (sssp) {dist, parent, depth}; } vector< int64 > solve(const Graph &g, int s) { int n = (int) g.size(); vector< int64 > dist(n, infll); UnionFind uf(n); using pi = tuple< int64, int, int >; priority_queue< pi, vector< pi >, greater<> > que; auto sp = dijkstra(g, s); vector< vector< int > > is_consistent(n); { queue< pair< int, int > > que2; que2.emplace(s, 0); vector< int > psi(n); while(not que2.empty()) { auto[u, bit] = que2.front(); que2.pop(); bool add = false; for(auto e : g[u]) { int v = e.to; if(sp.parent[v] == u and sp.dist[v] == sp.dist[u] + e.cost) { que2.emplace(v, bit ^ e.type); psi[e.to] = bit ^ e.type; add = true; if(psi[v]) { dist[v] = sp.dist[v]; } break; } } } for(int u = 0; u < n; u++) { for(auto e : g[u]) { int v = e.to; is_consistent[u].emplace_back((psi[u] ^ e.type) == psi[v]); } } } for(int u = 0; u < n; u++) { int i = 0; for(auto &e : g[u]) { int v = e.to; if(u < v and not is_consistent[u][i]) { que.emplace(sp.dist[u] + sp.dist[v] + e.cost, u, i); } ++i; } } while(not que.empty()) { auto[h, u0, i] = que.top(); que.pop(); int v0 = g[u0][i].to; int u = uf.find(u0); int v = uf.find(v0); vector< int > bs; while(u != v) { if(sp.depth[u] > sp.depth[v]) { bs.emplace_back(u); u = uf.find(sp.parent[u]); } else { bs.emplace_back(v); v = uf.find(sp.parent[v]); } } for(int x : bs) { uf.unite(u, x); chmin(dist[x], h - sp.dist[x]); int ptr = 0; for(auto &e : g[x]) { if(is_consistent[x][ptr]) { que.emplace(dist[x] + sp.dist[e.to] + e.cost, x, ptr); } ++ptr; } } } return dist; } int main() { int N, M, K; cin >> N >> M >> K; Graph g(N); for(int i = 0; i < M; i++) { int a, b, c; string s; cin >> a >> b >> c >> s; --a, --b; int d = 0; for(int j = 0; j < K; j++) { if(s[j] == '1') d |= 1 << j; } g[a].emplace_back((edge) {b, c, d, i}); g[b].emplace_back((edge) {a, c, d, i}); } auto shortest_path = solve(g, N - 1); for(int i = 0; i + 1 < N; i++) { if(shortest_path[i] >= infll) cout << -1 << "\n"; else cout << shortest_path[i] << "\n"; } }