#include using namespace std; #define rep(i, n) for(int i = 0; i < n; i++) #define rep2(i, x, n) for(int i = x; i <= n; i++) #define rep3(i, x, n) for(int i = x; i >= n; i--) #define each(e, v) for(auto &e: v) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define rall(x) x.rbegin(), x.rend() #define sz(x) (int)x.size() using ll = long long; using pii = pair; using pil = pair; using pli = pair; using pll = pair; const int MOD = 1000000007; //const int MOD = 998244353; const int inf = (1<<30)-1; const ll INF = (1LL<<60)-1; template bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;}; template bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;}; struct io_setup{ io_setup(){ ios_base::sync_with_stdio(false); cin.tie(NULL); cout << fixed << setprecision(15); } } io_setup; template struct Mod_Int{ int x; Mod_Int() : x(0) {} Mod_Int(ll y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Mod_Int &operator += (const Mod_Int &p){ if((x += p.x) >= mod) x -= mod; return *this; } Mod_Int &operator -= (const Mod_Int &p){ if((x += mod - p.x) >= mod) x -= mod; return *this; } Mod_Int &operator *= (const Mod_Int &p){ x = (int) (1LL * x * p.x % mod); return *this; } Mod_Int &operator /= (const Mod_Int &p){ *this *= p.inverse(); return *this; } Mod_Int &operator ++ () {return *this += Mod_Int(1);} Mod_Int operator ++ (int){ Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator -- () {return *this -= Mod_Int(1);} Mod_Int operator -- (int){ Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator - () const {return Mod_Int(-x);} Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;} Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;} Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;} Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;} bool operator == (const Mod_Int &p) const {return x == p.x;} bool operator != (const Mod_Int &p) const {return x != p.x;} Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod-2); } Mod_Int pow(ll k) const{ Mod_Int now = *this, ret = 1; for(; k; k >>= 1, now *= now){ if(k&1) ret *= now; } return ret; } friend ostream &operator << (ostream &os, const Mod_Int &p){ return os << p.x; } friend istream &operator >> (istream &is, Mod_Int &p){ ll a; is >> a; p = Mod_Int(a); return is; } }; using mint = Mod_Int; struct Graph{ struct edge{ int to; mint l, a; edge(int to, mint l, mint a) : to(to), l(l), a(a) {} }; vector> es, rs; vector tw, c1, c2; vector dp1, dp2; const int n; Graph(int n) : n(n){ es.resize(n), rs.resize(n); tw.assign(n, false), c1.assign(n, false), c2.assign(n, false); dp1.assign(n, 0), dp2.assign(n, 0); } void add_edge(int from, int to, mint l, mint a, bool directed = true){ es[from].eb(to, l, a), rs[to].eb(from, l, a); } void dfs(int now){ c1[now] = true; each(e, es[now]){ if(!c1[e.to]) dfs(e.to); } } void rfs(int now){ c2[now] = true; each(e, rs[now]){ if(!c2[e.to]) rfs(e.to); } } void solve(int s, int t){ dfs(s), rfs(t); rep(i, n){ if(tw[i] && c1[i] && c2[i]){ cout << "INF\n"; return; } } dp1[s] = 0, dp2[s] = 1; rep(i, n){ each(e, es[i]){ dp1[e.to] += dp1[i]*e.a+dp2[i]*e.a*e.l; dp2[e.to] += dp2[i]*e.a; } } cout << dp1[t] << '\n'; } }; struct Strongly_Connected_Components{ vector> es, rs; vector vs, comp; vector used; const int n; Strongly_Connected_Components(int n) : n(n){ es.resize(n), rs.resize(n); vs.resize(n), comp.resize(n), used.resize(n); } void add_edge(int from, int to, bool directed = false){ es[from].pb(to), rs[to].pb(from); if(!directed) es[to].pb(from), rs[from].pb(to); } void topological_sort(int now){ used[now] = true; each(e, es[now]) if(!used[e]) topological_sort(e); vs.pb(now); } void track_back(int now, int cnt){ used[now] = true, comp[now] = cnt; each(e, rs[now]) if(!used[e]) track_back(e, cnt); } Graph decompose(){ fill(all(used), false); rep(i, n) if(!used[i]) topological_sort(i); fill(all(used), false), reverse(all(vs)); int cnt = 0; each(e, vs) if(!used[e]) track_back(e, cnt++); Graph G(cnt); vector K(cnt, 0); rep(i, n) K[comp[i]]++; rep(i, cnt){ if(K[i] > 1) G.tw[i] = true; } /* rep(i, n){ each(e, es[i]){ int u = comp[i], v = comp[e]; if(u != v) G.add_edge(u, v, true); } } */ return G; } int operator [] (int k) const {return comp[k];} }; int main(){ int N, M; cin >> N >> M; vector u(M), v(M); vector l(M), a(M); Strongly_Connected_Components scc(N+1); rep(i, M){ cin >> u[i] >> v[i] >> l[i] >> a[i]; scc.add_edge(u[i], v[i], true); } Graph G = scc.decompose(); rep(i, M){ int U = scc[u[i]], V = scc[v[i]]; if(U != V) G.add_edge(U, V, l[i], a[i], true); } int s = scc[0], t = scc[N]; G.solve(s, t); }