#![allow(unused_imports)] use fact::*; use mod_int::*; use pio2::*; use std::{ collections::*, io::{self, prelude::*}, }; def_mint!(1000000007, Mod); fn run(mut pin: I, mut out: O) { let (n, m): (usize, usize) = pin.parse(); let f = Fact::::new(2 * n); let mut ans = f.binom(2 * n, n) * Mint::from(2 * n); for (t, x, y) in pin.seq::<(u32, usize, usize)>(m) { if t == 1 { ans -= f.binom(x + y, x) * f.binom((n - x - 1) + (n - y), n - y); } else { ans -= f.binom(x + y, y) * f.binom((n - x) + (n - y - 1), n - x); } } wln!(out, "{}", ans); } fn main() { let stdin = io::stdin(); let mut pin = Scanner::new(stdin.lock()); let stdout = io::stdout(); let mut out = stdout.lock(); run(&mut pin, &mut out); } pub mod fact { use super::mod_int::*; pub struct Fact { f: Vec>, finv: Vec>, } impl Fact { pub fn new(n: usize) -> Self { let mut f = vec![ModInt::new(0); n + 1]; f[0] = ModInt::new(1); for i in 1..=n { f[i] = ModInt::new(i as u32) * f[i - 1]; } let mut finv = vec![ModInt::new(0); n + 1]; finv[n] = f[n].inv(); for i in (1..=n).rev() { finv[i - 1] = finv[i] * ModInt::new(i as u32); } Self { f, finv } } pub fn fact(&self, x: usize) -> ModInt { self.f[x] } pub fn fact_inv(&self, x: usize) -> ModInt { self.finv[x] } pub fn binom(&self, n: usize, k: usize) -> ModInt { if n >= k { self.fact(n) * self.fact_inv(n - k) * self.fact_inv(k) } else { ModInt::new(0) } } pub fn perm(&self, n: usize, k: usize) -> ModInt { if n >= k { self.fact(n) * self.fact_inv(n - k) } else { ModInt::new(0) } } } } pub mod mod_int { use std::{cmp, fmt, marker::PhantomData, ops, sync::atomic}; #[macro_export] macro_rules! def_mint { ($modulo:expr, $ModuloTy:ident) => { pub struct $ModuloTy; impl crate::mod_int::Modulo for $ModuloTy { fn modulo() -> u32 { $modulo } } pub type Mint = crate::mod_int::ModInt<$ModuloTy>; pub fn mint(x: u32) -> Mint { crate::mod_int::ModInt::new(x) } }; } pub trait Modulo { fn modulo() -> u32; } pub struct VarMod; static VAR_MOD: atomic::AtomicU32 = atomic::AtomicU32::new(0); pub fn set_var_mod(m: u32) { VAR_MOD.store(m, atomic::Ordering::Relaxed); } impl Modulo for VarMod { fn modulo() -> u32 { VAR_MOD.load(atomic::Ordering::Relaxed) } } #[repr(transparent)] pub struct ModInt(u32, PhantomData<*const M>); impl ModInt { pub fn new(x: u32) -> Self { debug_assert!(x < M::modulo()); Self(x, PhantomData) } pub fn normalize(self) -> Self { if self.0 < M::modulo() { self } else { Self::new(self.0 % M::modulo()) } } pub fn get(self) -> u32 { self.0 } pub fn inv(self) -> Self { assert_ne!(self, Self::new(0)); self.pow(M::modulo() - 2) } pub fn half(self) -> Self { Self::new(self.0 / 2 + self.0 % 2 * ((M::modulo() + 1) / 2)) } pub fn modulo() -> u32 { M::modulo() } } impl ops::Neg for ModInt { type Output = Self; fn neg(self) -> Self { Self::new(if self.0 == 0 { 0 } else { M::modulo() - self.0 }) } } impl ops::Neg for &'_ ModInt { type Output = ModInt; fn neg(self) -> Self::Output { -(*self) } } impl ops::Add for ModInt { type Output = Self; fn add(self, rhs: Self) -> Self { let s = self.0 + rhs.0; Self::new(if s < M::modulo() { s } else { s - M::modulo() }) } } impl ops::Sub for ModInt { type Output = Self; fn sub(self, rhs: Self) -> Self { Self::new(if self.0 >= rhs.0 { self.0 - rhs.0 } else { M::modulo() + self.0 - rhs.0 }) } } impl ops::Mul for ModInt { type Output = Self; fn mul(self, rhs: Self) -> Self { Self::new((self.0 as u64 * rhs.0 as u64 % M::modulo() as u64) as u32) } } impl ops::Div for ModInt { type Output = Self; fn div(self, rhs: Self) -> Self { self * rhs.inv() } } macro_rules ! op_impl { ($ ($ Op : ident $ op : ident $ OpAssign : ident $ op_assign : ident) *) => { $ (impl < M : Modulo > ops ::$ Op <& Self > for ModInt < M > { type Output = Self ; fn $ op (self , rhs : & Self) -> Self { self .$ op (* rhs) } } impl < M : Modulo > ops ::$ Op < ModInt < M >> for & ModInt < M > { type Output = ModInt < M >; fn $ op (self , rhs : ModInt < M >) -> ModInt < M > { (* self) .$ op (rhs) } } impl < M : Modulo > ops ::$ Op <& ModInt < M >> for & ModInt < M > { type Output = ModInt < M >; fn $ op (self , rhs : & ModInt < M >) -> ModInt < M > { (* self) .$ op (* rhs) } } impl < M : Modulo > ops ::$ OpAssign for ModInt < M > { fn $ op_assign (& mut self , rhs : Self) { * self = ops ::$ Op ::$ op (* self , rhs) ; } } impl < M : Modulo > ops ::$ OpAssign <& ModInt < M >> for ModInt < M > { fn $ op_assign (& mut self , rhs : & ModInt < M >) { self .$ op_assign (* rhs) ; } }) * } ; } op_impl! { Add add AddAssign add_assign Sub sub SubAssign sub_assign Mul mul MulAssign mul_assign Div div DivAssign div_assign } impl std::iter::Sum for ModInt { fn sum>(iter: I) -> Self { iter.fold(ModInt::new(0), |x, y| x + y) } } impl std::iter::Product for ModInt { fn product>(iter: I) -> Self { iter.fold(ModInt::new(1), |x, y| x * y) } } pub trait Pow { fn pow(self, n: T) -> Self; } impl Pow for ModInt { fn pow(mut self, mut n: u32) -> Self { let mut y = Self::new(1); while n > 0 { if n % 2 == 1 { y *= self; } self *= self; n /= 2; } y } } macro_rules ! mod_int_pow_impl { ($ ($ T : ident) *) => { $ (impl < M : Modulo > Pow <$ T > for ModInt < M > { fn pow (self , n : $ T) -> Self { self . pow (n . rem_euclid (M :: modulo () as $ T - 1) as u32) } }) * } ; } mod_int_pow_impl ! (isize i32 i64 usize u64); macro_rules ! mod_int_from_impl { ($ ($ T : ident) *) => { $ (impl < M : Modulo > From <$ T > for ModInt < M > { # [allow (unused_comparisons)] fn from (x : $ T) -> Self { if M :: modulo () <= $ T :: max_value () as u32 { Self :: new (x . rem_euclid (M :: modulo () as $ T) as u32) } else if x < 0 { Self :: new ((M :: modulo () as i32 + x as i32) as u32) } else { Self :: new (x as u32) } } }) * } } mod_int_from_impl ! (isize i8 i16 i32 i64 i128 usize u8 u16 u32 u64 u128); impl From for ModInt { fn from(x: bool) -> Self { Self::new(x as u32) } } impl Copy for ModInt {} impl Clone for ModInt { fn clone(&self) -> Self { *self } } impl Default for ModInt { fn default() -> Self { Self::new(0) } } impl cmp::PartialEq for ModInt { fn eq(&self, other: &Self) -> bool { self.0 == other.0 } } impl cmp::Eq for ModInt {} impl cmp::PartialOrd for ModInt { fn partial_cmp(&self, other: &Self) -> Option { self.0.partial_cmp(&other.0) } } impl cmp::Ord for ModInt { fn cmp(&self, other: &Self) -> cmp::Ordering { self.0.cmp(&other.0) } } impl std::hash::Hash for ModInt { fn hash(&self, state: &mut H) { self.0.hash(state); } } impl fmt::Display for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { self.0.fmt(f) } } impl fmt::Debug for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { self.0.fmt(f) } } } pub mod macros { #[macro_export] macro_rules ! w { ($ ($ arg : tt) *) => { write ! ($ ($ arg) *) . unwrap () ; } } #[macro_export] macro_rules ! wln { ($ dst : expr $ (, $ ($ arg : tt) *) ?) => { { writeln ! ($ dst $ (, $ ($ arg) *) ?) . unwrap () ; # [cfg (debug_assertions)] $ dst . flush () . unwrap () ; } } } #[macro_export] macro_rules! w_iter { ($dst:expr, $fmt:expr, $iter:expr, $delim:expr) => {{ let mut first = true; for elem in $iter { if first { w!($dst, $fmt, elem); first = false; } else { w!($dst, concat!($delim, $fmt), elem); } } }}; ($dst:expr, $fmt:expr, $iter:expr) => { w_iter!($dst, $fmt, $iter, " ") }; } #[macro_export] macro_rules ! w_iter_ln { ($ dst : expr , $ ($ t : tt) *) => { { w_iter ! ($ dst , $ ($ t) *) ; wln ! ($ dst) ; } } } #[macro_export] macro_rules ! e { ($ ($ t : tt) *) => { # [cfg (debug_assertions)] eprint ! ($ ($ t) *) } } #[macro_export] macro_rules ! eln { ($ ($ t : tt) *) => { # [cfg (debug_assertions)] eprintln ! ($ ($ t) *) } } #[macro_export] macro_rules ! __tstr { ($ h : expr $ (, $ t : expr) +) => { concat ! (__tstr ! ($ ($ t) ,+) , ", " , __tstr ! (@)) } ; ($ h : expr) => { concat ! (__tstr ! () , " " , __tstr ! (@)) } ; () => { "\x1B[94m[{}:{}]\x1B[0m" } ; (@) => { "\x1B[1;92m{}\x1B[0m = {:?}" } } #[macro_export] macro_rules ! d { ($ ($ a : expr) ,*) => { eln ! (__tstr ! ($ ($ a) ,*) , file ! () , line ! () , $ (stringify ! ($ a) , $ a) ,*) } ; } } pub mod pio2 { use std::{ io::prelude::*, marker::PhantomData, mem::{self, MaybeUninit}, str, }; pub trait Input { fn bytes(&mut self) -> &[u8]; fn str(&mut self) -> &str { str::from_utf8(self.bytes()).unwrap() } fn parse(&mut self) -> T where DefaultParser: Parser, { self.parse_with(DefaultParser) } fn parse_with>(&mut self, mut parser: P) -> T { parser.parse(self) } fn seq(&mut self, n: usize) -> Seq where DefaultParser: Parser, { self.seq_with(n, DefaultParser) } fn seq_with>(&mut self, n: usize, parser: P) -> Seq { Seq { src: self, rest: n, parser, phantom: PhantomData, } } } impl Input for &mut I { fn bytes(&mut self) -> &[u8] { (**self).bytes() } } pub struct Scanner { src: R, buf: Vec, pos: usize, len: usize, } impl Scanner { pub fn new(src: R) -> Self { Self { src, buf: vec![0; 1 << 16], pos: 0, len: 0, } } fn read(&mut self) -> usize { if self.pos > 0 { self.buf.copy_within(self.pos..self.len, 0); self.len -= self.pos; self.pos = 0; } else if self.len >= self.buf.len() { self.buf.resize(2 * self.buf.len(), 0); } let n = self.src.read(&mut self.buf[self.len..]).unwrap(); self.len += n; assert!(self.len <= self.buf.len()); n } } impl Input for Scanner { fn bytes(&mut self) -> &[u8] { loop { while let Some(d) = unsafe { self.buf.get_unchecked(self.pos..self.len) } .iter() .position(u8::is_ascii_whitespace) { let p = self.pos; self.pos += d + 1; if d > 0 { return unsafe { self.buf.get_unchecked(p..p + d) }; } } if self.read() == 0 { let p = self.pos; if p == self.len { panic!("reached EOF"); } self.pos = self.len; return unsafe { self.buf.get_unchecked(p..self.len) }; } } } } pub struct Seq<'a, I: ?Sized, T, P> { src: &'a mut I, rest: usize, parser: P, phantom: PhantomData<*const T>, } impl<'a, I: Input + ?Sized, T, P: Parser> Iterator for Seq<'a, I, T, P> { type Item = T; fn next(&mut self) -> Option { if self.rest > 0 { self.rest -= 1; Some(self.src.parse_with(&mut self.parser)) } else { None } } fn size_hint(&self) -> (usize, Option) { (self.rest, Some(self.rest)) } } impl<'a, I: Input + ?Sized, T, P: Parser> ExactSizeIterator for Seq<'a, I, T, P> {} pub trait Parser { fn parse(&mut self, src: &mut I) -> T; } impl> Parser for &mut P { fn parse(&mut self, src: &mut I) -> T { (*self).parse(src) } } #[derive(Clone, Copy, Debug)] pub struct DefaultParser; macro_rules! int { ($ty:ident) => { impl Parser<$ty> for DefaultParser { fn parse(&mut self, src: &mut I) -> $ty { let f = |s: &[u8]| s.iter().fold(0, |x, b| 10 * x + (b & 0xf) as $ty); let s = src.bytes(); if let Some((&b'-', t)) = s.split_first() { -f(t) } else { f(s) } } } }; } int!(isize); int!(i8); int!(i16); int!(i32); int!(i64); int!(i128); macro_rules! uint { ($ty:ident) => { impl Parser<$ty> for DefaultParser { fn parse(&mut self, src: &mut I) -> $ty { src.bytes().iter().fold(0, |x, b| 10 * x + (b & 0xf) as $ty) } } }; } uint!(usize); uint!(u8); uint!(u16); uint!(u32); uint!(u64); uint!(u128); macro_rules! from_bytes { ($ty:ty) => { impl Parser<$ty> for DefaultParser { fn parse(&mut self, src: &mut I) -> $ty { src.bytes().into() } } }; } from_bytes!(Vec); from_bytes!(Box<[u8]>); macro_rules! from_str { ($ty:ident) => { impl Parser<$ty> for DefaultParser { fn parse(&mut self, src: &mut I) -> $ty { src.str().parse::<$ty>().expect("failed to parse") } } }; } from_str!(String); from_str!(char); from_str!(f32); from_str!(f64); macro_rules ! tuple { ($ ($ T : ident) ,+) => { impl <$ ($ T) ,+> Parser < ($ ($ T ,) +) > for DefaultParser where $ (DefaultParser : Parser <$ T >) ,+ { fn parse < I : Input + ? Sized > (& mut self , src : & mut I) -> ($ ($ T ,) +) { ($ (< Self as Parser <$ T >>:: parse (self , src) ,) +) } } } ; } tuple!(A); tuple!(A, B); tuple!(A, B, C); tuple!(A, B, C, D); tuple!(A, B, C, D, E); tuple!(A, B, C, D, E, F); tuple!(A, B, C, D, E, F, G); tuple!(A, B, C, D, E, F, G, H); macro_rules ! array { ($ ($ N : literal) *) => { $ (impl < T > Parser < [T ; $ N] > for DefaultParser where DefaultParser : Parser < T > { fn parse < I : Input + ? Sized > (& mut self , src : & mut I) -> [T ; $ N] { unsafe { let mut arr : [MaybeUninit < T >; $ N] = MaybeUninit :: uninit () . assume_init () ; for elem in & mut arr { * elem = MaybeUninit :: new (src . parse ()) ; } mem :: transmute_copy (& arr) } } }) * } } array ! (1 2 3 4 5 6 7 8); }