// >>> TEMPLATES #include using namespace std; using ll = long long; using ld = long double; using i32 = int32_t; using i64 = int64_t; using u32 = uint32_t; using u64 = uint64_t; #define int ll #define rep(i, n) for (int i = 0; i < (int)(n); i++) #define rep1(i, n) for (int i = 1; i <= (int)(n); i++) #define repR(i, n) for (int i = (int)(n)-1; i >= 0; i--) #define rep1R(i, n) for (int i = (int)(n); i >= 1; i--) #define loop(i, a, B) for (int i = a; i B; i++) #define loopR(i, a, B) for (int i = a; i B; i--) #define all(x) begin(x), end(x) #define allR(x) rbegin(x), rend(x) #define rng(x, l, r) begin(x) + (l), begin(x) + (r) #define pb push_back #define eb emplace_back #define fst first #define snd second template auto mp(A &&a, B &&b) { return make_pair(forward(a), forward(b)); } template auto mt(T&&... x) { return make_tuple(forward(x)...); } template auto constexpr inf_ = numeric_limits::max()/2-1; auto constexpr INF32 = inf_; auto constexpr INF64 = inf_; auto constexpr INF = inf_; #ifdef LOCAL #include "debug.hpp" #else #define dump(...) (void)(0) #define say(x) (void)(0) #define debug if (0) #endif template struct pque : priority_queue, Comp> { vector &data() { return this->c; } void clear() { this->c.clear(); } }; template using pque_max = pque>; template using pque_min = pque>; template ::value, int> = 0> ostream& operator<<(ostream& os, T const& a) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ::value, int> = 0> ostream& operator<<(ostream& os, const T (&a)[N]) { bool f = true; for (auto const& x : a) os << (f ? "" : " ") << x, f = false; return os; } template ())), class = typename enable_if::value>::type> istream& operator>>(istream& is, T &a) { for (auto& x : a) is >> x; return is; } template ostream& operator<<(ostream& os, pair const& p) { return os << p.first << " " << p.second; } template istream& operator>>(istream& is, pair& p) { return is >> p.first >> p.second; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(15); } } iosetup; template struct FixPoint : private F { constexpr FixPoint(F&& f) : F(forward(f)) {} template constexpr auto operator()(T&&... x) const { return F::operator()(*this, forward(x)...); } }; struct MakeFixPoint { template constexpr auto operator|(F&& f) const { return FixPoint(forward(f)); } }; #define MFP MakeFixPoint()| #define def(name, ...) auto name = MFP [&](auto &&name, __VA_ARGS__) template struct vec_impl { using type = vector::type>; template static type make_v(size_t n, U&&... x) { return type(n, vec_impl::make_v(forward(x)...)); } }; template struct vec_impl { using type = T; static type make_v(T const& x = {}) { return x; } }; template using vec = typename vec_impl::type; template auto make_v(Args&&... args) { return vec_impl::make_v(forward(args)...); } template void quit(T const& x) { cout << x << endl; exit(0); } template constexpr bool chmin(T& x, U const& y) { if (x > y) { x = y; return true; } return false; } template constexpr bool chmax(T& x, U const& y) { if (x < y) { x = y; return true; } return false; } template constexpr auto sumof(It b, It e) { return accumulate(b, e, typename iterator_traits::value_type{}); } template int sz(T const& x) { return x.size(); } template int lbd(C const& v, T const& x) { return lower_bound(begin(v), end(v), x)-begin(v); } template int ubd(C const& v, T const& x) { return upper_bound(begin(v), end(v), x)-begin(v); } const int dx[] = { 1, 0, -1, 0, 1, -1, -1, 1 }; const int dy[] = { 0, 1, 0, -1, 1, 1, -1, -1 }; constexpr int popcnt(ll x) { return __builtin_popcountll(x); } template pair operator+(pair const& p, pair const& q) { return { p.first + q.first, p.second + q.second }; } template pair operator-(pair const& p, pair const& q) { return { p.first - q.first, p.second - q.second }; } mt19937_64 seed_{random_device{}()}; template Int rand(Int a, Int b) { return uniform_int_distribution(a, b)(seed_); } i64 irand(i64 a, i64 b) { return rand(a, b); } // [a, b] u64 urand(u64 a, u64 b) { return rand(a, b); } // template void shuffle(It l, It r) { shuffle(l, r, seed_); } // <<< // >>> modint template class modint { static_assert(md < (1u<<31), ""); using M = modint; using i64 = int64_t; uint32_t x; public: static constexpr uint32_t mod = md; constexpr modint(i64 x = 0) : x((x%=md) < 0 ? x+md : x) { } constexpr i64 val() const { return x; } constexpr explicit operator i64() const { return x; } constexpr bool operator==(M r) const { return x == r.x; } constexpr bool operator!=(M r) const { return x != r.x; } constexpr M operator+() const { return *this; } constexpr M operator-() const { return M()-*this; } constexpr M& operator+=(M r) { x += r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator-=(M r) { x += md-r.x; x = (x < md ? x : x-md); return *this; } constexpr M& operator*=(M r) { x = (uint64_t(x)*r.x)%md; return *this; } constexpr M& operator/=(M r) { return *this *= r.inv(); } constexpr M operator+(M r) const { return M(*this) += r; } constexpr M operator-(M r) const { return M(*this) -= r; } constexpr M operator*(M r) const { return M(*this) *= r; } constexpr M operator/(M r) const { return M(*this) /= r; } friend constexpr M operator+(i64 x, M y) { return M(x)+y; } friend constexpr M operator-(i64 x, M y) { return M(x)-y; } friend constexpr M operator*(i64 x, M y) { return M(x)*y; } friend constexpr M operator/(i64 x, M y) { return M(x)/y; } constexpr M inv() const { assert(x > 0); return pow(md-2); } constexpr M pow(i64 n) const { assert(not (x == 0 && n == 0)); if (n < 0) return inv().pow(-n); M v = *this, r = 1; for (; n > 0; n >>= 1, v *= v) if (n&1) r *= v; return r; } #ifdef LOCAL friend string to_s(M r) { return to_s(r.val(), mod); } #endif friend ostream& operator<<(ostream& os, M r) { return os << r.val(); } friend istream& operator>>(istream& is, M &r) { i64 x; is >> x; r = x; return is; } }; // <<< //constexpr int64_t MOD = 998244353; constexpr int64_t MOD = 1e9+7; using mint = modint; mint parity(int n) { return n & 1 ? -1 : +1; } // >>> mod table template struct ModTable { vector fact = {1, 1}, finv = {1, 1}, inv = {0, 1}; void calc(int n) { int old = fact.size(); if (n < old) return; fact.resize(n+1); finv.resize(n+1); inv.resize(n+1); for (uint32_t i = old; i <= n; i++) { fact[i] = uint64_t(fact[i-1])*i % mod; inv[i] = mod - uint64_t(inv[mod%i])*(mod/i) % mod; finv[i] = uint64_t(finv[i-1])*inv[i] % mod; } } }; ModTable mod_tab; modint fact(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.fact[n]; } modint finv(int n) { assert(0 <= n); return mod_tab.calc(n), mod_tab.finv[n]; } modint comb(int n, int k) { if (n < 0 || k < 0 || n < k) return 0; return fact(n)*finv(k)*finv(n-k); } modint perm(int n, int k) { assert(k >= 0); assert(n >= k); return fact(n)*finv(n-k); } // <<< // >>> scc #ifndef EDGE_INFO #define EDGE_INFO constexpr int dest(int v) { return v; } template ().to)> constexpr int dest(E const& e) { return e.to; } constexpr int cost(int) { return 1; } template ().cost)> constexpr auto cost(E const& e) { return e.cost; } template using cost_t = decltype(cost(declval())); #endif template struct SCC { vector> const& g; vector ord, low, st; int32_t time = 0, pos = 0, sz = 0; SCC(vector> const& g) : g(g), ord(g.size()), low(g.size()), st(g.size()) { rep (v, g.size()) if (ord[v] == 0) dfs(v); for (auto &x : ord) x += sz; } void dfs(int32_t v) { low[v] = ord[v] = ++time; st[pos++] = v; for (auto const& e : g[v]) { if (ord[dest(e)] == 0) { dfs(dest(e)); chmin(low[v], low[dest(e)]); } else if (ord[dest(e)] > 0) { chmin(low[v], ord[dest(e)]); } } if (low[v] == ord[v]) { sz++; do ord[st[--pos]] = -sz; while (st[pos] != v); } } // t-sorted id int id(int v) const { return ord[v]; } int size() const { return sz; } vector> groups() const { vector> grp(sz); rep (v, g.size()) grp[ord[v]].push_back(v); return grp; } // no multiple edges, no self-loops // no edge information vector> graph() const { vector> ret(size()); rep (v, g.size()) { for (auto const& e : g[v]) { int x = id(v), y = id(dest(e)); if (x != y) ret[x].push_back(y); } } for (auto &ls : ret) { sort(ls.begin(), ls.end()); ls.erase(unique(ls.begin(), ls.end()), ls.end()); } return ret; } }; template auto get_scc(vector> const& g) { return SCC(g); } // <<< // >>> bfs #ifndef EDGE_INFO #define EDGE_INFO constexpr int dest(int v) { return v; } template ().to)> constexpr int dest(E const& e) { return e.to; } constexpr int cost(int) { return 1; } template ().cost)> constexpr auto cost(E const& e) { return e.cost; } template using cost_t = decltype(cost(declval())); #endif template vector bfs(vector> const& g, int s, int inf) { vector d(g.size(), inf); queue q; d[s] = 0; q.push(s); while (q.size()) { int x = q.front(); q.pop(); for (auto const& e : g[x]) { const int y = dest(e); if (chmin(d[y], d[x]+1)) q.push(y); } } return d; } // <<< int32_t main() { int n, m; cin >> n >> m; n++; struct edge { int to, len, num; }; vector> g(n), rg(n); rep (i, m) { int x, y, L, N; cin >> x >> y >> L >> N; g[x].pb({y, L, N}); rg[y].pb({x, L, N}); } auto scc = get_scc(g); auto h = scc.graph(); vector> rh(h.size()); rep (i, h.size()) for (int j : h[i]) { rh[j].eb(i); } auto grp = scc.groups(); auto ds = bfs(h, scc.id(0), INF); auto dt = bfs(rh, scc.id(n-1), INF); vector alive(h.size(), 0); // dump(h, grp); // dump(ds); // dump(dt); rep (i, h.size()) { alive[i] = (ds[i] < INF and dt[i] < INF); if (alive[i] and sz(grp[i]) >= 2) { quit("INF"); } } vector ord(n); iota(all(ord), 0); sort(all(ord), [&](int x, int y) { return scc.id(x) < scc.id(y); }); vector scnt(n); scnt[0] = 1; for (int x : ord) { if (not alive[scc.id(x)]) continue; for (auto [y, len, num] : g[x]) { if (not alive[scc.id(y)]) continue; scnt[y] += scnt[x] * num; } } reverse(all(ord)); vector tcnt(n); tcnt[n-1] = 1; for (int x : ord) { if (not alive[scc.id(x)]) continue; for (auto [y, len, num] : rg[x]) { if (not alive[scc.id(y)]) continue; tcnt[y] += tcnt[x] * num; } } dump(scnt); dump(tcnt); mint ans = 0; rep (x, n) for (auto [y, len, num] : g[x]) { ans += scnt[x] * tcnt[y] * num * len; } cout << ans << "\n"; }