diff --git a/yukicoder/2457.rs b/yukicoder/2457.rs new file mode 100644 index 00000000..f35c9a31 --- /dev/null +++ b/yukicoder/2457.rs @@ -0,0 +1,137 @@ +use std::cmp::*; +use std::io::Read; + +fn get_word() -> String { + let stdin = std::io::stdin(); + let mut stdin=stdin.lock(); + let mut u8b: [u8; 1] = [0]; + loop { + let mut buf: Vec = Vec::with_capacity(16); + loop { + let res = stdin.read(&mut u8b); + if res.unwrap_or(0) == 0 || u8b[0] <= b' ' { + break; + } else { + buf.push(u8b[0]); + } + } + if buf.len() >= 1 { + let ret = String::from_utf8(buf).unwrap(); + return ret; + } + } +} + +fn get() -> T { get_word().parse().ok().unwrap() } + +/// 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)] + pub 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

; + +fn freq(l: i64, k: i64, x: i64) -> MInt { + let ma = min(k, l - k + 1); + if x <= 0 || x > ma { + return 0.into(); + } + if x == ma { + return MInt::new((l - k + 1 - k).abs() + 1); + } + 2.into() +} + +fn main() { + let h: i64 = get(); + let w: i64 = get(); + let n: i64 = get(); + let k: i64 = get(); + let factor = MInt::new((h - k + 1) * (w - k + 1)).inv(); + let mut tot = MInt::new(0); + for i in 1..k + 1 { + for j in 1..k + 1 { + let p = factor * i * j; + tot += (-(-p + 1).pow(n) + 1) * freq(h, k, i) * freq(w, k, j); + } + } + println!("{}", tot); +}