#line 1 "d.cpp" #include using namespace std; #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #pragma GCC target("avx2") // 数値型 using ll = long long; using ull = unsigned long long; using ld = long double; using P = pair; using Pll = pair; using Pli = pair; using Pil = pair; // vector関連 using vi = vector; using vvi = vector; using vvvi = vector; using vll = vector; using vvll = vector; using vvvll = vector; template using vc = vector; template using vvc = vector>; template using vvvc = vector>; template using vvvvc = vector>; // priority_queue template using pq = priority_queue; template using pqg = priority_queue, greater>; #define rep(i, n) for(int i = 0; i < (int)(n); i++) #define FOR(i, a, b) for(int i = a; i < (int)(b); i++) #define all(a) (a).begin(),(a).end() #define rall(a) (a).rbegin(),(a).rend() #define MIN(vec) *min_element(vec) #define MAX(vec) *max_element(vec) #define next_perm(vec) next_permutation((vec).begin(), (vec).end()) #define UNIQUE(vec) vec.erase(unique(vec.begin(), vec.end()), vec.end()) #define el "\n" #define Yes cout << "Yes" << el #define No cout << "No" << el #define YES cout << "YES" << el #define NO cout << "NO" << el #define EPS 1e-8 #define Equal(a, b) (fabs((a)-(b)) < EPS) #define dbg(x) cerr << #x << "=" << x << el // 定数 const string abc = "abcdefghijklmnopqrstuvwxyz"; const string ABC = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; constexpr int INF = 1001001001; constexpr ll LINF = 1001001001001001001ll; constexpr int DX[] = {1, 0, -1, 0}; constexpr int DY[] = {0, 1, 0, -1}; constexpr int DX8[] = {1, 0, -1, 0, 1, 1, -1, -1}; constexpr int DY8[] = {0, 1, 0, -1, 1, -1, 1, -1}; template ostream &operator<< (ostream &os, pair p) { os << "{" << p.first << "," << p.second << "}"; return os; } template ostream &operator<< (ostream &os, vc &vec) { int sz = vec.size(); rep(i, sz){ os << vec[i] << (i==sz-1?"":" "); } return os; } template istream &operator>> (istream &is, pair &p) { is >> p.first >> p.second; return is; } template istream &operator>> (istream &is, vc &vec) { int sz = vec.size(); rep(i, sz) { is >> vec[i]; } return is; } /// @brief aとbの最大値をaに格納。更新があったかbool値を返す /// @tparam T1 /// @tparam T2 /// @param a /// @param b /// @return bool template inline bool chmax(T1 &a, T2 b){ bool ret = a inline bool chmin(T1 &a, T2 b){ bool ret = a>b; if(ret) {a = b;} return ret; } inline void YesNo(bool flag){ if(flag) {Yes;} else {No;} return; } inline void YESNO(bool flag){ if(flag) {YES;} else {NO;} return; } inline bool outof(ll x, ll xlim){ return (x<0 || x>=xlim); } template inline T sqnorm(T x, T y){ return x*x+y*y; } /// @brief char->int /// @param c /// @return int inline int ctoi(char c){ return c-'0'; } /// @brief xを素因数分解 /// @param x /// @return vector, 素因数の昇順に {p, cnt} vector prime_fact(ll x){ vector ret; for(ll i=2; i*i<=x; i++){ if(x%i == 0){ ret.emplace_back(i, 0); while(x%i == 0){ ret.back().second++; x /= i; } } } if(x != 1) ret.emplace_back(x, 1); return ret; } /// @brief xの約数列挙 /// @param x /// @return vll, 約数の昇順 vll divisor_enum(ll x){ vector ret; for(ll i=1; i*i<=x; i++){ if(x%i == 0){ ret.push_back(x/i); ret.push_back(i); } } sort(all(ret)); UNIQUE(ret); return ret; } /// @brief 繰り返し二乗法。 /// @tparam T /// @param x /// @param k /// @param op /// @param e /// @return template T pow_t(T x, ll k, T (*op)(T, T), T (*e)()){ T ret = e(); while(k){ if(k&1) ret = op(ret, x); x = op(x, x); k >>= 1; } return ret; } ll powll(ll x, ll k){ return pow_t(x, k, [](ll a, ll b) -> ll{return a*b;}, []() -> ll{return 1;}); } inline int pop_cnt(ll x) { return __builtin_popcountll(x); } inline int top_bit(ll x) { return (x==0?-1:63-__builtin_clzll(x));} void main2(); int main(){ ios::sync_with_stdio(false); std::cin.tie(nullptr); main2(); } #line 2 "/home/miie/kyopro/library/my-library/Math/Fraction/Fraction.hpp" template T gcd_t(T a, T b) { if(a < 0) a = -a; if(b < 0) b = -b; while(b != 0) { T r = a % b; a = b; b = r; } return a; } template struct Fraction { T num, den; Fraction(T num, T den): num(num), den(den) { if(num == 0) this->den = 1; else { T g = gcd_t(num, den); this->num /= g; this->den /= g; } } Fraction operator+(const Fraction &a) { return Fraction(num*a.den + den*a.num, den*a.den); } bool operator<(const Fraction &a) const { return num*a.den < den*a.num; } bool operator>(const Fraction &a) const { return num*a.den > den*a.num; } bool operator==(const Fraction &a) const { return num*a.den == den*a.num; } bool operator!=(const Fraction &a) const { return !(num*a.den == den*a.num); } }; #line 212 "d.cpp" #include namespace mp = boost::multiprecision; // 任意長整数型 using Bint = mp::cpp_int; void main2(){ int n, m; cin >> n >> m; using F = Fraction; struct Edge { int to; F w; }; vvc g(n); rep(i, m) { int u, v, a, b; cin >> u >> v >> a >> b; u--; v--; g[u].push_back({v, {a, b}}); g[v].push_back({u, {a, b}}); } pqg> que; vc dist(n, F{INF, 1}); dist[0] = F{0, 1}; que.push({F{0, 1}, 0}); int cnt = 0; while(!que.empty() && cnt < n) { auto [d, v] = que.top(); que.pop(); if(dist[v] != d) continue; cnt++; for(auto [nv, w] : g[v]) { auto f = d+w; if(chmin(dist[nv], d+w)) { que.push({dist[nv], nv}); } } } rep(i, n-1) { cout << dist[i+1].num << " " << dist[i+1].den << el; } }