// ---------- begin SegmentTree Point update Range query ---------- mod segment_tree { pub struct PURQ T> { n: usize, a: Vec, id: T, op: F, } #[allow(dead_code)] impl T> PURQ { pub fn new(n: usize, id: T, op: F) -> PURQ { let mut k = 1; while k < n { k *= 2; } PURQ { n: k, a: vec![id.clone(); 2 * k], id: id, op: op, } } pub fn update(&mut self, x: usize, v: T) { let mut k = self.n + x; let a = &mut self.a; a[k] = v; k >>= 1; while k > 0 { a[k] = (self.op)(a[2 * k].clone(), a[2 * k + 1].clone()); k >>= 1; } } pub fn update_tmp(&mut self, x: usize, v: T) { self.a[x + self.n] = v; } pub fn update_all(&mut self) { for k in (1..(self.n)).rev() { self.a[k] = (self.op)(self.a[2 * k].clone(), self.a[2 * k + 1].clone()); } } pub fn find(&self, mut l: usize, mut r: usize) -> T { let mut p = self.id.clone(); let mut q = self.id.clone(); l += self.n; r += self.n; while l < r { if (l & 1) == 1 { p = (self.op)(p, self.a[l].clone()); l += 1; } if (r & 1) == 1 { r -= 1; q = (self.op)(self.a[r].clone(), q); } l >>= 1; r >>= 1; } (self.op)(p, q) } } } // ---------- end SegmentTree Point update Range query ---------- // ---------- begin ModInt ---------- mod modint { #[allow(dead_code)] pub struct Mod; impl ConstantModulo for Mod { const MOD: u32 = 1_000_000_007; } #[allow(dead_code)] pub struct StaticMod; static mut STATIC_MOD: u32 = 0; impl Modulo for StaticMod { fn modulo() -> u32 { unsafe { STATIC_MOD } } } #[allow(dead_code)] impl StaticMod { pub fn set_modulo(p: u32) { unsafe { STATIC_MOD = p; } } } use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub trait ConstantModulo { const MOD: u32; } impl Modulo for T where T: ConstantModulo, { fn modulo() -> u32 { T::MOD } } pub struct ModInt(pub u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { ModInt::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut d = self.0 + rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl AddAssign for ModInt { fn add_assign(&mut self, rhs: Self) { *self = *self + rhs; } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Self) -> Self::Output { let mut d = T::modulo() + self.0 - rhs.0; if d >= T::modulo() { d -= T::modulo(); } ModInt::new_unchecked(d) } } impl SubAssign for ModInt { fn sub_assign(&mut self, rhs: Self) { *self = *self - rhs; } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Self) -> Self::Output { let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64; ModInt::new_unchecked(v as u32) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Self) { *self = *self * rhs; } } impl Neg for ModInt { type Output = ModInt; fn neg(self) -> Self::Output { if self.0 == 0 { Self::zero() } else { Self::new_unchecked(T::modulo() - self.0) } } } impl std::fmt::Display for ModInt { fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result { write!(f, "{}", self.0) } } impl std::str::FromStr for ModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let val = s.parse::()?; Ok(ModInt::new(val)) } } impl From for ModInt { fn from(val: usize) -> ModInt { ModInt::new_unchecked((val % T::modulo() as usize) as u32) } } impl From for ModInt { fn from(val: u64) -> ModInt { ModInt::new_unchecked((val % T::modulo() as u64) as u32) } } impl From for ModInt { fn from(val: i64) -> ModInt { let m = T::modulo() as i64; ModInt::new((val % m + m) as u32) } } #[allow(dead_code)] impl ModInt { pub fn new_unchecked(d: u32) -> Self { ModInt(d, PhantomData) } pub fn zero() -> Self { ModInt::new_unchecked(0) } pub fn one() -> Self { ModInt::new_unchecked(1) } pub fn is_zero(&self) -> bool { self.0 == 0 } } #[allow(dead_code)] impl ModInt { pub fn new(d: u32) -> Self { ModInt::new_unchecked(d % T::modulo()) } pub fn pow(&self, mut n: u64) -> Self { let mut t = Self::one(); let mut s = *self; while n > 0 { if n & 1 == 1 { t *= s; } s *= s; n >>= 1; } t } pub fn inv(&self) -> Self { assert!(self.0 != 0); self.pow(T::modulo() as u64 - 2) } } #[allow(dead_code)] pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 { let mut t = 1 % m; let mut s = r % m; while n > 0 { if n & 1 == 1 { t = t * s % m; } s = s * s % m; n >>= 1; } t } } // ---------- end ModInt ---------- // ---------- begin Precalc ---------- mod precalc { use super::modint::*; #[allow(dead_code)] pub 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) { fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32); } ifact[n] = fact[n].inv(); if n > 0 { inv[n] = ifact[n] * fact[n - 1]; } for i in (1..n).rev() { ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32); inv[i] = ifact[i] * fact[i - 1]; } Precalc { inv: inv, fact: fact, ifact: ifact, } } pub fn inv(&self, n: usize) -> ModInt { assert!(n > 0); 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 perm(&self, n: usize, k: usize) -> ModInt { if k > n { return ModInt::zero(); } self.fact[n] * self.ifact[n - k] } 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 ---------- //https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // // P_i != 0 な条件は // L <= x <= R でA = 0 がないことを表す // またR_i != R_j の条件からRだけ残しとけば残りは自由に割り振ってもok // // 非ゼロが確定してるものを除いた列でP_i = 0 の条件を考えれば良い // なんかみたことある形... // 包含関係にある条件があったらでかい方を除く // use std::collections::*; use std::ops::Bound::*; use modint::*; type M = ModInt; fn run() { input! { n: usize, m: usize, cond: [(usize1, usize, i32); m], } let mut set = (0..n).collect::>(); let mut zero = vec![]; for (l, r, p) in cond { if p == 0 { zero.push((l, r)); continue; } let mut del = vec![]; for &v in set.range((Included(&l), Excluded(&r))) { del.push(v); } for v in del { set.remove(&v); } } for &(l, r) in zero.iter() { if set.range((Included(&l), Excluded(&r))).next().is_none() { println!("0"); return; } } let free = n - set.len() - (m - zero.len()); let mut a = vec![false; n + 1]; let mut cnt = vec![0; n + 1]; for v in set { a[v] = true; cnt[v] = 1; } for i in (0..n).rev() { cnt[i] += cnt[i + 1]; } zero.sort_by_key(|p| p.1); let mut cond: Vec<(usize, usize)> = vec![]; for &(l, r) in zero.iter().rev() { while cond.last().map_or(false, |p| p.0 <= l) { cond.pop(); } cond.push((l, r)); } let mut g = vec![None; n]; for (l, r) in cond { g[l] = Some(r); } let mut seg = segment_tree::PURQ::new(n + 1, (M::zero(), M::one()), |a, b| { (a.0 + b.0 * a.1, a.1 * b.1) }); for i in 0..n { seg.update_tmp(i, (M::zero(), if a[i] {M::new(2)} else {M::one()})); } seg.update_all(); let mut dp = vec![M::zero(); n + 1]; dp[n] = M::one(); for (i, g) in g.iter().enumerate().rev() { if a[i] { dp[i] = dp[i + 1] * M::new(3); } else { dp[i] = dp[i + 1]; } if let Some(r) = *g { let v = dp[r] * M::new(2).pow(cnt[i] - cnt[r]) - seg.find(i, r).0; seg.update(i, (v, if a[i] {M::new(2)} else {M::one()})); dp[i] = dp[i] - v; } } let ans = dp[0] * M::new(2).pow(free as u64); println!("{}", ans); } fn main() { run(); }