//@formatter:off #include #define overload4(_1,_2,_3,_4,name,...) name #define rep1(i,n) for (ll i = 0; i < ll(n); ++i) #define rep2(i,s,n) for (ll i = ll(s); i < ll(n); ++i) #define rep3(i,s,n,d) for(ll i = ll(s); i < ll(n); i+=d) #define rep(...) overload4(__VA_ARGS__,rep3,rep2,rep1)(__VA_ARGS__) #define rrep(i,n) for (ll i = ll(n)-1; i >= 0; i--) #define all(a) a.begin(),a.end() #define rall(a) a.rbegin(),a.rend() #define pb push_back #define eb emplace_back #ifdef __LOCAL #define debug(...) { cout << #__VA_ARGS__; cout << ": "; print(__VA_ARGS__); cout << flush; } #else #define debug(...) void(0) #endif #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) using namespace std; using ll = long long; using ld = long double; using P = pair; using LP = pair; using vi = vector; using vvi = vector>; using vl = vector; using vvl = vector>; using vd = vector; using vvd = vector>; using vs = vector; using vc = vector; using vvc = vector>; using vb = vector; using vvb = vector>; using vp = vector

; using vvp = vector>; template istream& operator>>(istream &is,pair &p) { return is >> p.first >> p.second; } template ostream& operator<<(ostream &os,const pair &p) { return os<<'{'< istream& operator>>(istream &is,vector &v) { for(T &t:v){is>>t;} return is; } template ostream& operator<<(ostream &os,const vector &v) { os<<'[';rep(i,v.size())os< bool chmin(T& a,T b) {if(a > b){a = b; return true;} return false;} template bool chmax(T& a,T b) {if(a < b){a = b; return true;} return false;} void scan(){} template void scan(Head& head, Tail&... tail){ cin >> head; scan(tail...); } template void print(const T& t){ cout << t << '\n'; } template void print(const Head& head, const Tail&... tail){ cout< void fin(T a) { print(a); exit(0); } const string yes[] = {"no","yes"}; const string Yes[] = {"No","Yes"}; const string YES[] = {"NO","YES"}; const int inf = 1001001001; const ll linf = 1001001001001001001; //@formatter:on constexpr int mod = 1000000007; //constexpr int mod = 998244353; struct mint { ll x; constexpr mint(ll x = 0) : x((x % mod + mod) % mod) {} constexpr mint operator-() const { return mint(-x); } constexpr mint &operator+=(const mint &a) { if ((x += a.x) >= mod) x -= mod; return *this; } constexpr mint &operator++() { return *this += mint(1); } constexpr mint &operator-=(const mint &a) { if ((x += mod - a.x) >= mod) x -= mod; return *this; } constexpr mint &operator--() { return *this -= mint(1); } constexpr mint &operator*=(const mint &a) { (x *= a.x) %= mod; return *this; } constexpr mint operator+(const mint &a) const { mint res(*this); return res += a; } constexpr mint operator-(const mint &a) const { mint res(*this); return res -= a; } constexpr mint operator*(const mint &a) const { mint res(*this); return res *= a; } constexpr mint pow(ll t) const { mint res = mint(1), a(*this); while (t > 0) { if (t & 1) res *= a; t >>= 1; a *= a; } return res; } // for prime mod constexpr mint inv() const { return pow(mod - 2); } constexpr mint &operator/=(const mint &a) { return *this *= a.inv(); } constexpr mint operator/(const mint &a) const { mint res(*this); return res /= a; } }; ostream &operator<<(ostream &os, const mint &a) { return os << a.x; } bool operator==(const mint &a, const mint &b) { return a.x == b.x; } bool operator!=(const mint &a, const mint &b) { return a.x != b.x; } bool operator==(const mint &a, const int &b) { return a.x == b; } bool operator!=(const mint &a, const int &b) { return a.x != b; } struct edge { int to, l, a; edge(int to, int l, int a) : to(to), l(l), a(a) {} }; mint dp[100010]; mint cnt[100010]; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); cout.tie(nullptr); INT(n, m); n++; vector> G(n); vector> rG(n); rep(_, m) { INT(u, v, l, a); G[u].eb(v, l, a); rG[v].eb(u, l, a); } vb ok(n, false); ok[n - 1] = true; queue q; q.push(n - 1); while (!q.empty()) { int u = q.front(); q.pop(); for (auto &e : rG[u]) { if (ok[e.to]) continue; ok[e.to] = true; q.push(e.to); } } if (!ok[0]) fin(0); vb nok(n, false); nok[0] = true; q.push(0); while (!q.empty()) { int u = q.front(); q.pop(); for (auto &e : G[u]) { if (nok[e.to]) continue; nok[e.to] = true; q.push(e.to); } } assert(nok[n - 1]); rep(i, n) ok[i] = ok[i] & nok[i]; vi in(n); int sz = 0; rep(i, n) { if (!ok[i]) continue; sz++; for (auto &e : G[i]) { if (!ok[e.to]) continue; in[e.to]++; } } vi ord; rep(i, n) if (ok[i] and !in[i]) q.push(i); while (!q.empty()) { int u = q.front(); assert(ok[u]); q.pop(); ord.pb(u); for (auto &e : G[u]) { if (!ok[e.to]) continue; if (--in[e.to] == 0) q.push(e.to); } } if (ord.size() < sz) fin("INF"); assert(ord.size() == sz); assert(ord[0] == 0); assert(ord.back() == n - 1); vi pos(n, -1); rep(i, sz) pos[ord[i]] = i; cnt[0] = 1; rep(i, sz) { if (cnt[i] == 0) continue; int now = ord[i]; for (auto &e : G[now]) { if (!ok[e.to]) continue; int nx = pos[e.to]; assert(nx > i); cnt[nx] += cnt[i] * e.a; dp[nx] += dp[i] * e.a + cnt[i] * e.a * e.l; } } print(dp[sz - 1]); }