#![allow(unused_imports)] #![allow(non_snake_case, unused)] use std::cmp::*; use std::collections::*; use std::ops::*; // https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254 より macro_rules! eprint { ($($t:tt)*) => {{ use ::std::io::Write; let _ = write!(::std::io::stderr(), $($t)*); }}; } macro_rules! eprintln { () => { eprintln!(""); }; ($($t:tt)*) => {{ use ::std::io::Write; let _ = writeln!(::std::io::stderr(), $($t)*); }}; } macro_rules! dbg { ($v:expr) => {{ let val = $v; eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val); val }} } macro_rules! mat { ($($e:expr),*) => { Vec::from(vec![$($e),*]) }; ($($e:expr,)*) => { Vec::from(vec![$($e),*]) }; ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) }; ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) }; } macro_rules! ok { ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => { $a$([$i])*.$f($($t),*) }; ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { { let t = $e; ok!($a$([$i])*.$f($($es),*)$(@$t)*@t) } }; } pub fn readln() -> String { let mut line = String::new(); ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e)); line } macro_rules! read { ($($t:tt),*; $n:expr) => {{ let stdin = ::std::io::stdin(); let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| { let line = line.unwrap(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }).collect::>(); ret }}; ($($t:tt),*) => {{ let line = readln(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }}; } macro_rules! _read { ($it:ident; [char]) => { _read!($it; String).chars().collect::>() }; ($it:ident; [u8]) => { Vec::from(_read!($it; String).into_bytes()) }; ($it:ident; usize1) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::().unwrap_or_else(|e| panic!("{}", e)) - 1 }; ($it:ident; [usize1]) => { $it.map(|s| s.parse::().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::>() }; ($it:ident; [$t:ty]) => { $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::>() }; ($it:ident; $t:ty) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e)) }; ($it:ident; $($t:tt),+) => { ($(_read!($it; $t)),*) }; } pub fn main() { let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join(); } // const MOD: usize = 998244353; const MOD: usize = 1_000_000_007; const INF: i64 = std::i64::MAX; // const INF: i128 = std::i128::MAX/100; #[derive(Clone, Copy)] struct ModInt(usize); impl std::ops::Add for ModInt { type Output = ModInt; fn add(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::AddAssign for ModInt { fn add_assign(&mut self, rhs: ModInt) { *self = *self + rhs; } } impl std::ops::Sub for ModInt { type Output = ModInt; fn sub(self, rhs: ModInt) -> Self::Output { let mut d = self.0 + MOD - rhs.0; if d >= MOD { d -= MOD; } ModInt(d) } } impl std::ops::SubAssign for ModInt { fn sub_assign(&mut self, rhs: ModInt) { *self = *self - rhs; } } impl std::ops::Mul for ModInt { type Output = ModInt; fn mul(self, rhs: ModInt) -> Self::Output { ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as usize) } } impl std::ops::MulAssign for ModInt { fn mul_assign(&mut self, rhs: ModInt) { *self = *self * rhs; } } impl std::ops::Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { ModInt(if self.0 == 0 {0} else {MOD - self.0}) } } /* impl std::fmt::Display for ModInt { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.0) } } */ #[allow(dead_code)] impl ModInt { pub fn new(n: usize) -> ModInt { ModInt(n % MOD) } pub fn zero() -> ModInt { ModInt(0) } pub fn one() -> ModInt { ModInt(1) } pub fn pow(self, mut n: usize) -> ModInt { let mut t = ModInt::one(); let mut s = self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(self) -> ModInt { self.pow(MOD - 2) } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- #[allow(dead_code)] struct Precalc { inv: Vec, fact: Vec, ifact: Vec, } #[allow(dead_code)] impl Precalc { pub fn new(n: usize) -> Precalc { let mut inv = vec![ModInt::one(); n + 1]; let mut fact = vec![ModInt::one(); n + 1]; let mut ifact = vec![ModInt::one(); n + 1]; for i in 2..(n + 1) { inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as usize); fact[i] = fact[i - 1] * ModInt(i as usize); ifact[i] = ifact[i - 1] * inv[i]; } Precalc { inv: inv, fact: fact, ifact: ifact, } } pub fn inv(&self, n: usize) -> ModInt { self.inv[n] } pub fn fact(&self, n: usize) -> ModInt { self.fact[n] } pub fn ifact(&self, n: usize) -> ModInt { self.ifact[n] } pub fn comb(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[k] * self.ifact[n - k] } } // ---------- end Precalc ---------- fn solve() { let (n,m) = read!(usize,usize); let uvla = read!(usize,usize,usize,usize;m); let mut tmp = vec![vec![];n+1]; let mut edge = vec![vec![];n+1]; for &(u,v,l,a) in &uvla { tmp[u].push((v,l,a)); } for i in 0..n+1 { let mut t = vec![]; for &(v,l,a) in &tmp[i] { t.push(v); } t.sort(); t.dedup(); let mut list = vec![(0,0);t.len()]; let mut map = HashMap::new(); for j in 0..t.len() { map.insert(t[j],j); } for &(v,l,a) in &tmp[i] { let idx = *map.get(&v).unwrap(); list[idx].0 += l*a; list[idx].1 += a; } for j in 0..t.len() { edge[i].push((t[j],list[j].0,list[j].1)); } } let mut inner = vec![0;n+1]; for i in 0..n+1 { for &(v,_,_) in &edge[i] { inner[v] += 1; } } let mut q = VecDeque::new(); for i in 0..n+1 { if inner[i]==0 { q.push_back(i); } } let mut list = vec![]; while let Some(cur) = q.pop_front() { list.push(cur); for &(e,_,_) in &edge[cur] { inner[e] -= 1; if inner[e]==0 { q.push_back(e); } } } let mut dp = vec![ModInt(0);n+1]; let mut pat = vec![ModInt(0);n+1]; let mut seen = vec![false;n+1]; pat[0] = ModInt(1); seen[0] = true; for &cur in &list { if !seen[cur] { continue; } for &(v,l,a) in &tmp[cur] { seen[v] = true; dp[v] = dp[v] + dp[cur]*ModInt(a) + ModInt(a)*ModInt(l)*pat[cur]; pat[v] = pat[v] + pat[cur]*ModInt(a); } } let mut seen2 = vec![false;n+1]; seen2[0] = true; let mut q = VecDeque::new(); q.push_back(0); while let Some(cur) = q.pop_front() { for &(v,_,_) in &edge[cur] { if !seen2[v] { q.push_back(v); seen2[v] = true; } } } if seen2[n] && !seen[n]{ println!("INF"); return; } println!("{}",dp[n].0); } fn run() { let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); solve(); }