use modint::ModInt998244353; use proconio::input; type Mint = ModInt998244353; const B: usize = 1_000_000; fn main() { // precalc(); input! { n: u32, k: u32 } let m = Mint::modulus(); let (n1, n0) = (n / m, n % m); let (k1, k0) = (k / m, k % m); let ans = binom(n0, k0) * binom(n1, k1); println!("{ans}"); } fn binom(n: u32, k: u32) -> Mint { if n < k { return 0.into(); } fact(n) / fact(k) / fact(n - k) } fn fact(n: u32) -> Mint { assert!(n < Mint::modulus()); let q = n as usize / B; let offset = (q * B) as u32; let mut fact = Mint::raw(TABLE[q]); for i in offset + 1..=n { fact *= i; } fact } #[allow(unused)] fn precalc() { let mut table = vec![1]; let mut fact = Mint::raw(1); for i in 1..Mint::modulus() as usize { fact *= i; if i % B == 0 { table.push(fact.val()); } } println!("const TABLE: [u32; {}] = [", table.len()); for chunk in table.chunks(8) { for x in chunk { print!("{x}, "); } println!(); } println!("];"); } #[allow(unused)] mod modint { use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign}; const fn gcd_inv(a: i64, b: i64) -> (i64, i64) { let a = a.rem_euclid(b); if a == 0 { return (b, 0); } // invariant: u.0 = u.1 * a (mod b) // invariant: v.0 = v.1 * a (mod b) let mut u = (b, 0); let mut v = (a, 1); while v.0 != 0 { let q = u.0.div_euclid(v.0); u.0 -= q * v.0; u.1 -= q * v.1; (u, v) = (v, u); } if u.1 < 0 { u.1 += b.div_euclid(u.0); } u } pub trait Modulus: 'static + Clone + Copy { const MOD: u32; } macro_rules! define_modulus { ( $( ($name:ident, $modulus:expr) ),* $(,)? ) => { $( #[derive(Clone, Copy, Debug, PartialEq, Eq)] pub struct $name; impl Modulus for $name { // TODO: use inline const for static assertion in Rust >= 1.79 // const MOD: u32 = const { assert!($modulus < (1u32 << 31)); $modulus }; const MOD: u32 = $modulus; } )* }; } define_modulus!((Mod998244353, 998244353), (Mod1000000007, 1000000007)); #[derive(Clone, Copy, PartialEq, Eq, Hash)] pub struct StaticModInt { val: u32, _phantom: std::marker::PhantomData M>, } impl StaticModInt { pub const fn modulus() -> u32 { M::MOD } pub const fn new(val: u32) -> Self { Self { val: val.rem_euclid(Self::modulus()), _phantom: std::marker::PhantomData, } } pub const fn raw(val: u32) -> Self { Self { val, _phantom: std::marker::PhantomData, } } pub const fn val(&self) -> u32 { self.val } pub const fn pow(self, mut exp: u64) -> Self { let modulus = Self::modulus() as u64; let mut base = self.val() as u64; let mut acc = 1u64; while exp > 0 { if exp & 1 == 1 { acc = acc * base % modulus; } base = base * base % modulus; exp >>= 1; } Self::raw(acc as u32) } pub const fn inv(self) -> Self { let Some(inv) = self.checked_inv() else { panic!() }; inv } pub const fn checked_inv(self) -> Option { let (gcd, inv) = gcd_inv(self.val() as i64, Self::modulus() as i64); if gcd == 1 { Some(Self::raw(inv as u32)) } else { None } } /// invariant: x.0 == val * x.1 (mod M) for x = u,v /// https://en.wikipedia.org/wiki/Rational_reconstruction_(mathematics) fn into_rational(&self) -> (i64, i64) { let m = Self::modulus() as i64; let mut u = (m, 0i64); let mut v = (self.val() as i64, 1i64); while v.0 * v.0 * 2 > m { let q = u.0.div_euclid(v.0); let w = (u.0 - q * v.0, u.1 - q * v.1); u = std::mem::replace(&mut v, w); } if v.1 < 0 { (-v.0, -v.1) } else { v } } } impl std::fmt::Display for StaticModInt { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { write!(f, "{}", self.val) } } impl std::fmt::Debug for StaticModInt { fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result { let (num, denom) = self.into_rational(); if denom == 1 { write!(f, "{num}") } else { write!(f, "{num}/{denom}") } } } impl std::str::FromStr for StaticModInt { type Err = std::num::ParseIntError; fn from_str(s: &str) -> Result { let value = s.parse::()?; Ok(value.into()) } } macro_rules! impl_from_integer { ( $( $ty:tt ),* ) => { $( impl From<$ty> for StaticModInt { fn from(value: $ty) -> StaticModInt { Self::raw((value as $ty).rem_euclid(Self::modulus() as $ty) as u32) } } )* }; } impl_from_integer!(u32, u64, usize, i32, i64, isize); impl std::ops::Neg for StaticModInt { type Output = Self; fn neg(mut self) -> Self::Output { if self.val > 0 { self.val = Self::modulus() - self.val; } self } } impl>> AddAssign for StaticModInt { fn add_assign(&mut self, rhs: T) { self.val += rhs.into().val; if self.val >= Self::modulus() { self.val -= Self::modulus(); } } } impl>> SubAssign for StaticModInt { fn sub_assign(&mut self, rhs: T) { self.val = self.val.wrapping_sub(rhs.into().val); if self.val > Self::modulus() { self.val = self.val.wrapping_add(Self::modulus()); } } } impl>> MulAssign for StaticModInt { fn mul_assign(&mut self, rhs: T) { self.val = ((self.val as u64 * rhs.into().val as u64) % Self::modulus() as u64) as u32; } } impl>> DivAssign for StaticModInt { fn div_assign(&mut self, rhs: T) { *self *= rhs.into().inv(); } } macro_rules! impl_binnary_operators { ( $({ $op: ident, $op_assign: ident, $fn: ident, $fn_assign: ident}),* $(,)? ) => { $( impl>> std::ops::$op for StaticModInt { type Output = StaticModInt; fn $fn(mut self, rhs: T) -> StaticModInt { self.$fn_assign(rhs.into()); self } } impl std::ops::$op<&StaticModInt> for StaticModInt { type Output = StaticModInt; fn $fn(self, rhs: &StaticModInt) -> StaticModInt { self.$fn(*rhs) } } impl>> std::ops::$op for &StaticModInt { type Output = StaticModInt; fn $fn(self, rhs: T) -> StaticModInt { (*self).$fn(rhs.into()) } } impl std::ops::$op<&StaticModInt> for &StaticModInt { type Output = StaticModInt; fn $fn(self, rhs: &StaticModInt) -> StaticModInt { (*self).$fn(*rhs) } } impl std::ops::$op_assign<&StaticModInt> for StaticModInt { fn $fn_assign(&mut self, rhs: &StaticModInt) { *self = self.$fn(*rhs); } } )* }; } impl_binnary_operators!( {Add, AddAssign, add, add_assign}, {Sub, SubAssign, sub, sub_assign}, {Mul, MulAssign, mul, mul_assign}, {Div, DivAssign, div, div_assign}, ); impl std::iter::Sum for StaticModInt { fn sum>(iter: I) -> Self { iter.fold(Self::raw(0), Add::add) } } impl<'a, M: Modulus> std::iter::Sum<&'a StaticModInt> for StaticModInt { fn sum>(iter: I) -> Self { iter.fold(Self::raw(0), Add::add) } } impl std::iter::Product for StaticModInt { fn product>(iter: I) -> Self { iter.fold(Self::raw(1), Mul::mul) } } impl<'a, M: Modulus> std::iter::Product<&'a StaticModInt> for StaticModInt { fn product>(iter: I) -> Self { iter.fold(Self::raw(1), Mul::mul) } } pub type ModInt998244353 = StaticModInt; pub type ModInt1000000007 = StaticModInt; } const TABLE: [u32; 999] = [ 1, 373341033, 45596018, 834980587, 623627864, 428937595, 442819817, 499710224, 833655840, 83857087, 295201906, 788488293, 671639287, 849315549, 597398273, 813259672, 732727656, 244038325, 122642896, 310517972, 160030060, 483239722, 683879839, 712910418, 384710263, 433880730, 844360005, 513089677, 101492974, 959253371, 957629942, 678615452, 34035221, 56734233, 524027922, 31729117, 102311167, 330331487, 8332991, 832392662, 545208507, 594075875, 318497156, 859275605, 300738984, 767818091, 864118508, 878131539, 316588744, 812496962, 213689172, 584871249, 980836133, 54096741, 417876813, 363266670, 335481797, 730839588, 393495668, 435793297, 760025067, 811438469, 720976283, 650770098, 586537547, 117371703, 566486504, 749562308, 708205284, 932912293, 939830261, 983699513, 206579820, 301188781, 593164676, 770845925, 247687458, 41047791, 266419267, 937835947, 506268060, 6177705, 936268003, 166873118, 443834893, 328979964, 470135404, 954410105, 117565665, 832761782, 39806322, 478922755, 394880724, 821825588, 468705875, 512554988, 232240472, 876497899, 356048018, 895187265, 808258749, 575505950, 68190615, 939065335, 552199946, 694814243, 385460530, 529769387, 640377761, 916128300, 440133909, 362216114, 826373774, 502324157, 457648395, 385510728, 904737188, 78988746, 454565719, 623828097, 686156489, 713476044, 63602402, 570334625, 681055904, 222059821, 477211096, 343363294, 833792655, 461853093, 741797144, 74731896, 930484262, 268372735, 941222802, 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