use std::marker::*; use std::ops::*; pub trait Modulo { fn modulo() -> u32; } pub struct ConstantModulo; impl Modulo for ConstantModulo<{ M }> { fn modulo() -> u32 { M } } pub struct ModInt(u32, PhantomData); impl Clone for ModInt { fn clone(&self) -> Self { Self::new_unchecked(self.0) } } impl Copy for ModInt {} impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Self) -> Self::Output { let mut v = self.0 + rhs.0; if v >= T::modulo() { v -= T::modulo(); } Self::new_unchecked(v) } } 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 v = self.0 - rhs.0; if self.0 < rhs.0 { v += T::modulo(); } Self::new_unchecked(v) } } 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; Self::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.is_zero() { 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::fmt::Debug 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 ModInt { pub fn new_unchecked(n: u32) -> Self { ModInt(n, 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 } } 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.is_zero()); self.pow(T::modulo() as u64 - 2) } } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 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") }; } // ---------- end input macro ---------- type M = ModInt>; fn run() { input! { n: usize, k: usize, m: usize, p: [(usize1, usize); m], } let mut p = p; p.sort_by_key(|p| (p.1, !p.0)); p.dedup_by(|a, b| a.0 <= b.0); // dp[x][y]: x個使った、最後に使ったのがy な方法の数 let mut dp = vec![vec![M::zero(); k + 1]; k + 1]; let mut sum = vec![M::zero(); k + 1]; dp[0][k] = M::one(); sum[0] = M::one(); let mut last = k + 1; let mut x = p.len(); for i in (0..k).rev() { for j in (1..=k).rev() { dp[j][i] = sum[j - 1]; sum[j] = sum[j] + sum[j - 1]; } if x > 0 && p[x - 1].0 == i { let r = p[x - 1].1; for p in r..last { for j in 0..=k { sum[j] -= dp[j][p]; } } last = r; x -= 1; } } let mut pow = vec![M::zero(); k + 1]; for i in 0..=k { pow[i] = M::new(i as u32).pow(n as u64); } let mut binom = vec![M::zero(); k + 1]; binom[0] = M::one(); let mut ans = M::zero(); for (len, way) in sum.iter().enumerate().skip(1) { for i in (1..=len).rev() { binom[i] = binom[i] + binom[i - 1]; } let mut v = M::zero(); let mut sign = M::one(); for j in (1..=len).rev() { v += sign * binom[j] * pow[j]; sign = -sign; } ans += v * *way; } println!("{}", ans); } fn main() { run(); }