#include #include #include #include #include #include #include #include #include static const int MOD = 1000000007; using ll = long long; using u32 = unsigned; using u64 = unsigned long long; using namespace std; template constexpr T INF = ::numeric_limits::max() / 32 * 15 + 208; template struct modint { u32 val; public: static modint raw(int v) { modint x; x.val = v; return x; } modint() : val(0) {} template modint(T v) { ll x = (ll)(v%(ll)(M)); if (x < 0) x += M; val = u32(x); } modint(bool v) { val = ((unsigned int)(v) % M); } modint& operator++() { val++; if (val == M) val = 0; return *this; } modint& operator--() { if (val == 0) val = M; val--; return *this; } modint operator++(int) { modint result = *this; ++*this; return result; } modint operator--(int) { modint result = *this; --*this; return result; } modint& operator+=(const modint& b) { val += b.val; if (val >= M) val -= M; return *this; } modint& operator-=(const modint& b) { val -= b.val; if (val >= M) val += M; return *this; } modint& operator*=(const modint& b) { u64 z = val; z *= b.val; val = (u32)(z % M); return *this; } modint& operator/=(const modint& b) { return *this = *this * b.inv(); } modint operator+() const { return *this; } modint operator-() const { return modint() - *this; } modint pow(long long n) const { modint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } modint inv() const { return pow(M-2); } friend modint operator+(const modint& a, const modint& b) { return modint(a) += b; } friend modint operator-(const modint& a, const modint& b) { return modint(a) -= b; } friend modint operator*(const modint& a, const modint& b) { return modint(a) *= b; } friend modint operator/(const modint& a, const modint& b) { return modint(a) /= b; } friend bool operator==(const modint& a, const modint& b) { return a.val == b.val; } friend bool operator!=(const modint& a, const modint& b) { return a.val != b.val; } }; using mint = modint; int main() { int n, m; cin >> n >> m; n++; vector>> G(n), G2(n); vector deg(n); for (int i = 0; i < m; ++i) { int u, v, l, a; scanf("%d %d %d %d", &u, &v, &l, &a); G[u].emplace_back(array{v, l, a}); G2[v].emplace_back(array{u, l, a}); } { // 0 -> x; vector visited(n); visited[0] = 1; queue Q; Q.emplace(0); while(!Q.empty()){ int i = Q.front(); Q.pop(); for (auto &&e : G[i]) { if(!visited[e[0]]) { visited[e[0]] = 1; Q.emplace(e[0]); } } } for (int i = 0; i < n; ++i) { if(!visited[i]) deg[i] = -INF; } } { // x -> n vector visited(n); visited[n-1] = 1; queue Q; Q.emplace(n-1); while(!Q.empty()){ int i = Q.front(); Q.pop(); for (auto &&e : G2[i]) { if(!visited[e[0]]) { visited[e[0]] = 1; Q.emplace(e[0]); } } } if(!visited[0]){ puts("0"); return 0; } for (int i = 0; i < n; ++i) { if(!visited[i]) deg[i] = -INF; } } vector dp(n), dp2(n); mint ans = 0; { // x -> n auto degg = deg; for (int i = 0; i < n; ++i) { if(degg[i] >= 0){ for (auto &&e : G2[i]) { degg[e[0]]++; } } } vector Q; if(degg[n-1]){ puts("INF"); return 0; } Q.emplace_back(n-1); dp2[n-1] = 1; while(!Q.empty()){ int i = Q.back(); Q.pop_back(); for (auto &&e : G2[i]) { dp2[e[0]] += dp2[i]*e[2]; if(!(--degg[e[0]])) Q.emplace_back(e[0]); } } } { // 0 -> x for (int i = 0; i < n; ++i) { if(deg[i] >= 0){ for (auto &&e : G[i]) { deg[e[0]]++; } } } vector Q; if(deg[0]){ puts("INF"); return 0; } Q.emplace_back(0); dp[0] = 1; while(!Q.empty()){ int i = Q.back(); Q.pop_back(); for (auto &&e : G[i]) { dp[e[0]] += dp[i]*e[2]; ans += (dp[i]*dp2[e[0]]*e[1])*e[2]; if(!(--deg[e[0]])) Q.emplace_back(e[0]); } } } for (int i = 0; i < n; ++i) { if(deg[i] > 0) { puts("INF"); return 0; } } cout << ans.val << "\n"; return 0; }