// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ($(read_value!($next, $t)),*) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl Default for ModInt { fn default() -> Self { Self::new_internal(0) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl ::std::fmt::Debug for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { let (mut a, mut b, _) = red(self.x, M::m()); if b < 0 { a = -a; b = -b; } write!(f, "{}/{}", a, b) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } // Finds the simplest fraction x/y congruent to r mod p. // The return value (x, y, z) satisfies x = y * r + z * p. fn red(r: i64, p: i64) -> (i64, i64, i64) { if r.abs() <= 10000 { return (r, 1, 0); } let mut nxt_r = p % r; let mut q = p / r; if 2 * nxt_r >= r { nxt_r -= r; q += 1; } if 2 * nxt_r <= -r { nxt_r += r; q -= 1; } let (x, z, y) = red(nxt_r, r); (x, y - q * z, z) } } // mod mod_int macro_rules! define_mod { ($struct_name: ident, $modulo: expr) => { #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)] struct $struct_name {} impl mod_int::Mod for $struct_name { fn m() -> i64 { $modulo } } } } const MOD: i64 = 1_000_000_007; define_mod!(P, MOD); type MInt = mod_int::ModInt

; // Strong connected components. // Verified by: yukicoder No.470 (http://yukicoder.me/submissions/145785) // ABC214-H (https://atcoder.jp/contests/abc214/submissions/25082618) struct SCC { n: usize, ncc: usize, g: Vec>, // graph in adjacent list rg: Vec>, // reverse graph cmp: Vec, // topological order } impl SCC { fn new(n: usize) -> Self { SCC { n: n, ncc: n + 1, g: vec![Vec::new(); n], rg: vec![Vec::new(); n], cmp: vec![0; n], } } fn add_edge(&mut self, from: usize, to: usize) { self.g[from].push(to); self.rg[to].push(from); } fn dfs(&self, v: usize, used: &mut [bool], vs: &mut Vec) { used[v] = true; for &w in self.g[v].iter() { if !used[w] { self.dfs(w, used, vs); } } vs.push(v); } fn rdfs(&self, v: usize, k: usize, used: &mut [bool], cmp: &mut [usize]) { used[v] = true; cmp[v] = k; for &w in self.rg[v].iter() { if !used[w] { self.rdfs(w, k, used, cmp); } } } fn scc(&mut self) -> usize { let n = self.n; let mut used = vec![false; n]; let mut vs = Vec::new(); let mut cmp = vec![0; n]; for v in 0 .. n { if !used[v] { self.dfs(v, &mut used, &mut vs); } } for u in used.iter_mut() { *u = false; } let mut k = 0; for &t in vs.iter().rev() { if !used[t] { self.rdfs(t, k, &mut used, &mut cmp); k += 1; } } self.ncc = k; self.cmp = cmp; k } #[allow(dead_code)] fn top_order(&self) -> Vec { assert!(self.ncc <= self.n); self.cmp.clone() } /* * Returns a dag whose vertices are scc's, and whose edges are those of the original graph. */ #[allow(dead_code)] fn dag(&self) -> Vec> { assert!(self.ncc <= self.n); let ncc = self.ncc; let mut ret = vec![vec![]; ncc]; let n = self.n; for i in 0 .. n { for &to in self.g[i].iter() { if self.cmp[i] != self.cmp[to] { assert!(self.cmp[i] < self.cmp[to]); ret[self.cmp[i]].push(self.cmp[to]); } } } ret.into_iter().map(|mut v| { v.sort_unstable(); v.dedup(); v }).collect() } #[allow(dead_code)] fn rdag(&self) -> Vec> { assert!(self.ncc <= self.n); let ncc = self.ncc; let mut ret = vec![vec![]; ncc]; let n = self.n; for i in 0 .. n { for &to in self.g[i].iter() { if self.cmp[i] != self.cmp[to] { assert!(self.cmp[i] < self.cmp[to]); ret[self.cmp[to]].push(self.cmp[i]); } } } ret.into_iter().map(|mut v| { v.sort_unstable(); v.dedup(); v }).collect() } } trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); } impl Change for T { fn chmax(&mut self, x: T) { if *self < x { *self = x; } } fn chmin(&mut self, x: T) { if *self > x { *self = x; } } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); } fn reach(v: usize, g: &[Vec]) -> Vec { let n = g.len(); let mut vis = vec![false; n]; let mut que = vec![v]; while let Some(v) = que.pop() { if vis[v] { continue; } vis[v] = true; for &w in &g[v] { que.push(w); } } vis } fn dfs(v: usize, g: &[Vec<(usize, i64, i64)>], vis: &mut [bool], dp: &mut [(MInt, MInt)]) { if vis[v] { return; } let n = g.len(); if v == n - 1 { dp[v] = (1.into(), 0.into()); vis[v] = true; return; } let mut x = MInt::new(0); let mut y = MInt::new(0); for &(w, l, a) in &g[v] { dfs(w, g, vis, dp); x += dp[w].0 * a; y += (dp[w].1 + dp[w].0 * l) * a; } dp[v] = (x, y); vis[v] = true; } fn solve() { input! { n: usize, m: usize, uvla: [(usize, usize, i64, i64); m], } let mut scc = SCC::new(n + 1); for &(u, v, _, _) in &uvla { scc.add_edge(u, v); } let ncc = scc.scc(); let top_ord = scc.top_order(); let v1 = reach(top_ord[0], &scc.dag()); let v2 = reach(top_ord[n], &scc.rdag()); let mut sz = vec![0; ncc]; for i in 0..n + 1 { sz[top_ord[i]] += 1; } for i in 0..ncc { if v1[i] && v2[i] && sz[i] >= 2 { println!("INF"); return; } } let mut dp = vec![(MInt::new(0), MInt::new(0)); n + 1]; let mut vis = vec![false; n + 1]; let mut g = vec![vec![]; n + 1]; for &(u, v, l, a) in &uvla { let nu = top_ord[u]; let nv = top_ord[v]; if !v1[nu] || !v2[nu] || !v1[nv] || !v2[nv] { continue; } g[u].push((v, l, a)); } dfs(0, &g, &mut vis, &mut dp); println!("{}", dp[n].1); }