#[allow(unused_imports)] use std::cmp::*; // 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::<$t>().expect("Parse error")); } /// Verified by https://atcoder.jp/contests/abc198/submissions/21774342 mod mod_int { use std::ops::*; pub trait Mod: Copy { fn m() -> i64; } #[derive(Copy, Clone, Hash, PartialEq, Eq, PartialOrd, Ord)] pub struct ModInt { pub x: i64, phantom: ::std::marker::PhantomData } impl ModInt { // x >= 0 pub fn new(x: i64) -> Self { ModInt::new_internal(x % M::m()) } fn new_internal(x: i64) -> Self { ModInt { x: x, phantom: ::std::marker::PhantomData } } pub fn pow(self, mut e: i64) -> Self { debug_assert!(e >= 0); let mut sum = ModInt::new_internal(1); let mut cur = self; while e > 0 { if e % 2 != 0 { sum *= cur; } cur *= cur; e /= 2; } sum } #[allow(dead_code)] pub fn inv(self) -> Self { self.pow(M::m() - 2) } } impl Default for ModInt { fn default() -> Self { Self::new_internal(0) } } impl>> Add for ModInt { type Output = Self; fn add(self, other: T) -> Self { let other = other.into(); let mut sum = self.x + other.x; if sum >= M::m() { sum -= M::m(); } ModInt::new_internal(sum) } } impl>> Sub for ModInt { type Output = Self; fn sub(self, other: T) -> Self { let other = other.into(); let mut sum = self.x - other.x; if sum < 0 { sum += M::m(); } ModInt::new_internal(sum) } } impl>> Mul for ModInt { type Output = Self; fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) } } impl>> AddAssign for ModInt { fn add_assign(&mut self, other: T) { *self = *self + other; } } impl>> SubAssign for ModInt { fn sub_assign(&mut self, other: T) { *self = *self - other; } } impl>> MulAssign for ModInt { fn mul_assign(&mut self, other: T) { *self = *self * other; } } impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { ModInt::new(0) - self } } impl ::std::fmt::Display for ModInt { fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result { self.x.fmt(f) } } impl From for ModInt { fn from(x: i64) -> Self { Self::new(x) } } } // mod mod_int macro_rules! define_mod { ($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 = 998_244_353; define_mod!(P, MOD); type MInt = mod_int::ModInt

; // Depends on MInt.rs fn fact_init(w: usize) -> (Vec, Vec) { let mut fac = vec![MInt::new(1); w]; let mut invfac = vec![0.into(); w]; for i in 1..w { fac[i] = fac[i - 1] * i as i64; } invfac[w - 1] = fac[w - 1].inv(); for i in (0..w - 1).rev() { invfac[i] = invfac[i + 1] * (i as i64 + 1); } (fac, invfac) } trait Bisect { fn lower_bound(&self, val: &T) -> usize; fn upper_bound(&self, val: &T) -> usize; } impl Bisect for [T] { fn lower_bound(&self, val: &T) -> usize { let mut pass = self.len() + 1; let mut fail = 0; while pass - fail > 1 { let mid = (pass + fail) / 2; if &self[mid - 1] >= val { pass = mid; } else { fail = mid; } } pass - 1 } fn upper_bound(&self, val: &T) -> usize { let mut pass = self.len() + 1; let mut fail = 0; while pass - fail > 1 { let mid = (pass + fail) / 2; if &self[mid - 1] > val { pass = mid; } else { fail = mid; } } pass - 1 } } fn calc(mut v: Vec<(usize, usize)>, a: usize, b: usize, fac: &[MInt], invfac: &[MInt]) -> Vec { v.sort(); let n = v.len(); let mut dp = vec![vec![MInt::new(0); n + 1]; n + 2]; dp[0][0] = 1.into(); for i in 1..n + 2 { let ami = if i < n + 1 { 1 } else { 0 }; let (xi, yi) = if i < n + 1 { v[i - 1] } else { (a, b) }; for j in 0..i { let (xj, yj) = if j == 0 { (0, 0) } else { v[j - 1] }; if yj > yi { continue; } let comb = fac[xi + yi - xj - yj] * invfac[xi - xj] * invfac[yi - yj]; for k in ami..n + 1 { let val = dp[j][k - ami]; dp[i][k] += val * comb; } } } let mut ans = dp[n + 1].clone(); for i in (0..n + 1).rev() { for j in i + 1..n + 1 { ans[i] = ans[i] - ans[j] * invfac[j - i] * fac[j] * invfac[i]; } } ans } // https://yukicoder.me/problems/no/1354 (3.5) // 区間ごとに包除原理で O(M + L^2)? -> K 回まで通っていいのを忘れていた。DP で O(M + L^3) // Tags: inclusion-exclusion-principle fn main() { input! { n: usize, m: usize, l: usize, k: usize, xyc: [(usize, usize); m], xyt: [(usize, usize); l], } let (fac, invfac) = fact_init(2 * n + l + 1); let mut pts = vec![vec![]; m + 1]; for &xy in &xyt { let idx = xyc.upper_bound(&xy); pts[idx].push(xy); } let mut dp = vec![MInt::new(1)]; for i in 0..m + 1 { let (xlo, ylo) = if i == 0 { (0, 0) } else { xyc[i - 1] }; let (xhi, yhi) = if i == m { (n, n) } else { xyc[i] }; let mut v = vec![]; for &(x, y) in &pts[i] { if xlo <= x && x <= xhi && ylo <= y && y <= yhi { v.push((x - xlo, y - ylo)); } } if v.is_empty() { let factor = fac[xhi - xlo + yhi - ylo] * invfac[xhi - xlo] * invfac[yhi - ylo]; for elem in &mut dp { *elem *= factor; } continue; } let sub = calc(v, xhi - xlo, yhi - ylo, &fac, &invfac); let a = dp.len() - 1; let b = sub.len() - 1; let mut ep = vec![MInt::new(0); a + b + 1]; for j in 0..a + 1 { for k in 0..b + 1 { ep[j + k] += dp[j] * sub[k]; } } dp = ep; } let mut tot = MInt::new(0); for i in 0..min(dp.len(), k + 1) { tot += dp[i]; } println!("{}", tot); }