#![allow(unused_imports)] use input::*; use std::{ collections::*, io::{self, BufWriter, Write}, }; def_mint!(998244353); fn run(mut ss: I, mut out: O) { let (n, x, y): (usize, usize, usize) = ss.parse(); let (x, y) = if x < y { (x, y) } else { (y, x) }; let x = if x == 1 { 1 } else { x + 1 } as isize; let y = if y == n { n } else { y - 1 } as isize; let d = y - x; if d < 0 { wln!(out, "0"); return; } let m = d as usize; let mut c = vec![mint(0); m + 1]; c[0] = mint(1); for i in 1..=m { c[i] = c[i - 1]; if i >= 3 { c[i] = c[i] + c[i - 3]; } } wln!(out, "{}", c[m]); } fn main() { let stdin = io::stdin(); let ss = SplitWs::new(stdin.lock()); let stdout = io::stdout(); let out = BufWriter::new(stdout.lock()); run(ss, out); } pub mod mod_int { use std::{ cmp, fmt::{self, Debug, Display}, hash::Hash, iter::{Product, Sum}, marker::PhantomData, mem, ops::*, }; pub struct ModInt { x: u32, marker: PhantomData<*const M>, } pub trait Modulo { fn modulo() -> u32; } impl ModInt { pub fn new(x: u32) -> Self { Self { x, marker: PhantomData, } } pub fn get(self) -> u32 { self.x } } impl ModInt { pub fn modulo() -> u32 { M::modulo() } pub fn normalize(self) -> Self { Self::new(self.x % M::modulo()) } pub fn inv(self) -> Self { assert_ne!(self.get(), 0); self.pow(M::modulo() - 2) } pub fn twice(self) -> Self { self + self } pub fn half(self) -> Self { if self.x & 1 == 0 { Self::new(self.x >> 1) } else { Self::new((self.x >> 1) + ((Self::modulo() + 1) >> 1)) } } } impl Clone for ModInt { fn clone(&self) -> Self { Self::new(self.x) } } impl Copy for ModInt {} impl Neg for ModInt { type Output = Self; fn neg(self) -> Self { Self::new(if self.x != 0 { M::modulo() - self.x } else { 0 }) } } impl Neg for &ModInt { type Output = ModInt; fn neg(self) -> Self::Output { -(*self) } } impl Add for ModInt { type Output = Self; fn add(self, rhs: Self) -> Self { let x = self.x + rhs.x; Self::new(if x < M::modulo() { x } else { x - M::modulo() }) } } impl Sub for ModInt { type Output = Self; fn sub(self, rhs: Self) -> Self { let x = if self.x >= rhs.x { self.x - rhs.x } else { M::modulo() + self.x - rhs.x }; Self::new(x) } } impl Mul for ModInt { type Output = Self; fn mul(self, rhs: Self) -> Self { let x = (self.x as u64 * rhs.x as u64) % M::modulo() as u64; Self::new(x as u32) } } impl Div for ModInt { type Output = Self; #[allow(clippy::suspicious_arithmetic_impl)] fn div(self, rhs: Self) -> Self { self * rhs.inv() } } macro_rules! biops { ($ Op : ident , $ op : ident , $ OpAssign : ident , $ op_assign : ident) => { impl $Op<&Self> for ModInt { type Output = Self; fn $op(self, rhs: &Self) -> Self { self.$op(*rhs) } } impl $Op> for &ModInt { type Output = ModInt; fn $op(self, rhs: ModInt) -> ModInt { (*self).$op(rhs) } } impl $Op for &ModInt { type Output = ModInt; fn $op(self, rhs: Self) -> ModInt { (*self).$op(*rhs) } } impl $OpAssign for ModInt { fn $op_assign(&mut self, rhs: Self) { *self = self.$op(rhs); } } impl $OpAssign<&Self> for ModInt { fn $op_assign(&mut self, rhs: &Self) { *self = self.$op(rhs); } } }; } biops!(Add, add, AddAssign, add_assign); biops!(Sub, sub, SubAssign, sub_assign); biops!(Mul, mul, MulAssign, mul_assign); biops!(Div, div, DivAssign, div_assign); impl Sum for ModInt { fn sum>(iter: I) -> Self { iter.fold(ModInt::new(0), |x, y| x + y) } } impl Product for ModInt { fn product>(iter: I) -> Self { iter.fold(ModInt::new(1), |x, y| x * y) } } macro_rules! fold { ($ Trait : ident , $ f : ident) => { impl<'a, M: Modulo + 'a> $Trait<&'a ModInt> for ModInt { fn $f>>(iter: I) -> Self { iter.copied().$f() } } }; } fold!(Sum, sum); fold!(Product, product); pub trait Pow { fn pow(self, exp: Exp) -> Self; } macro_rules! pow { ($ uty : ident , $ ity : ident) => { impl Pow<$uty> for ModInt { fn pow(self, mut exp: $uty) -> Self { if exp == 0 { return ModInt::new(1); } let mut res = ModInt::new(1); let mut base = self; while exp > 1 { if exp & 1 != 0 { res *= base; } exp >>= 1; base *= base; } base * res } } impl Pow<$ity> for ModInt { fn pow(self, exp: $ity) -> Self { if exp >= 0 { self.pow(exp as $uty) } else { self.inv().pow(-exp as $uty) } } } }; } macro_rules ! impls { ($ m : ident , $ ($ uty : ident , $ ity : ident) ,*) => { $ ($ m ! ($ uty , $ ity) ;) * } ; } impls!(pow, usize, isize, u8, i8, u16, i16, u32, i32, u64, i64, u128, i128); impl Default for ModInt { fn default() -> Self { Self::new(0) } } impl PartialEq for ModInt { fn eq(&self, other: &Self) -> bool { self.x == other.x } } impl Eq for ModInt {} impl PartialOrd for ModInt { fn partial_cmp(&self, other: &Self) -> Option { self.x.partial_cmp(&other.x) } } impl Ord for ModInt { fn cmp(&self, other: &Self) -> cmp::Ordering { self.x.cmp(&other.x) } } impl Hash for ModInt { fn hash(&self, state: &mut H) { self.x.hash(state) } } macro_rules! from_uint { ($ ty : ident) => { impl From<$ty> for ModInt { fn from(x: $ty) -> Self { if mem::size_of::<$ty>() <= 4 { if ($ty::max_value() as u32) < M::modulo() { Self::new(x as u32) } else { Self::new(x as u32).normalize() } } else { Self::new((x % M::modulo() as $ty) as u32) } } } }; } macro_rules ! impls { ($ m : ident , $ ($ ty : ident) ,*) => { $ ($ m ! ($ ty) ;) * } ; } impls!(from_uint, usize, u8, u16, u32, u64, u128); macro_rules! from_small_int { ($ ty : ident) => { impl From<$ty> for ModInt { fn from(x: $ty) -> Self { let mut x = x as i32; if x >= 0 { Self::from(x as u32) } else { while x < 0 { x += M::modulo() as i32; } Self::new(x as u32) } } } }; } impls!(from_small_int, i8, i16, i32); impl Display for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { Display::fmt(&self.x, f) } } impl Debug for ModInt { fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result { Debug::fmt(&self.x, f) } } #[macro_export] macro_rules! def_mint { ($ modulo : expr) => { #[derive(Clone, Copy, PartialEq, Eq, Default, Debug)] pub struct MintModulo; impl crate::mod_int::Modulo for MintModulo { fn modulo() -> u32 { $modulo } } pub type Mint = crate::mod_int::ModInt; pub fn mint>(x: T) -> Mint { x.into() } }; } } pub mod input { use std::{ io::{self, prelude::*}, marker::PhantomData, mem, }; pub trait Input { fn bytes(&mut self) -> &[u8]; fn bytes_vec(&mut self) -> Vec { self.bytes().to_vec() } fn str(&mut self) -> &str { std::str::from_utf8(self.bytes()).unwrap() } fn parse(&mut self) -> T { self.parse_with(DefaultParser) } fn parse_with(&mut self, mut parser: impl Parser) -> T { parser.parse(self) } fn seq(&mut self) -> Seq { self.seq_with(DefaultParser) } fn seq_with>(&mut self, parser: P) -> Seq { Seq { input: self, parser, marker: PhantomData, } } } impl Input for &mut T { fn bytes(&mut self) -> &[u8] { (**self).bytes() } } pub trait Parser { fn parse(&mut self, s: &mut I) -> T; } impl> Parser for &mut P { fn parse(&mut self, s: &mut I) -> T { (**self).parse(s) } } pub trait Parse { fn parse(s: &mut I) -> Self; } pub struct DefaultParser; impl Parser for DefaultParser { fn parse(&mut self, s: &mut I) -> T { T::parse(s) } } pub struct Seq<'a, T, I: ?Sized, P> { input: &'a mut I, parser: P, marker: PhantomData<*const T>, } impl<'a, T, I: Input, P: Parser> Iterator for Seq<'a, T, I, P> { type Item = T; #[inline] fn next(&mut self) -> Option { Some(self.input.parse_with(&mut self.parser)) } fn size_hint(&self) -> (usize, Option) { (!0, None) } } impl Parse for char { #[inline] fn parse(s: &mut I) -> Self { let s = s.bytes(); debug_assert_eq!(s.len(), 1); *s.first().expect("zero length") as char } } macro_rules ! tuple { ($ ($ T : ident) ,*) => { impl <$ ($ T : Parse) ,*> Parse for ($ ($ T ,) *) { # [inline] # [allow (unused_variables)] # [allow (clippy :: unused_unit)] fn parse < I : Input + ? Sized > (s : & mut I) -> Self { ($ ($ T :: parse (s) ,) *) } } } ; } tuple!(); 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); #[cfg(feature = "newer")] impl Parse for [T; N] { fn parse(s: &mut I) -> Self { use std::{mem::MaybeUninit, ptr}; struct Guard { arr: [MaybeUninit; N], i: usize, } impl Drop for Guard { fn drop(&mut self) { unsafe { ptr::drop_in_place(&mut self.arr[..self.i] as *mut _ as *mut [T]); } } } let mut g = Guard:: { arr: unsafe { MaybeUninit::uninit().assume_init() }, i: 0, }; while g.i < N { g.arr[g.i] = MaybeUninit::new(s.parse()); g.i += 1; } unsafe { mem::transmute_copy(&g.arr) } } } macro_rules! uint { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { let s = s.bytes(); s.iter().fold(0, |x, d| 10 * x + (0xf & d) as $ty) } } }; } macro_rules! int { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { let f = |s: &[u8]| { s.iter() .fold(0 as $ty, |x, d| (10 * x).wrapping_add((0xf & d) as $ty)) }; let s = s.bytes(); if let [b'-', s @ ..] = s { f(s).wrapping_neg() } else { f(s) } } } }; } macro_rules! float { ($ ty : ty) => { impl Parse for $ty { fn parse(s: &mut I) -> Self { const POW: [$ty; 18] = [ 1e0, 1e1, 1e2, 1e3, 1e4, 1e5, 1e6, 1e7, 1e8, 1e9, 1e10, 1e11, 1e12, 1e13, 1e14, 1e15, 1e16, 1e17, ]; let s = s.bytes(); let (minus, s) = if let Some((b'-', s)) = s.split_first() { (true, s) } else { (false, s) }; let (int, fract) = if let Some(p) = s.iter().position(|c| *c == b'.') { (&s[..p], &s[p + 1..]) } else { (s, &[][..]) }; let x = int .iter() .chain(fract) .fold(0u64, |x, d| 10 * x + (0xf & *d) as u64); let x = x as $ty; let x = if minus { -x } else { x }; let exp = fract.len(); if exp == 0 { x } else if let Some(pow) = POW.get(exp) { x / pow } else { x / (10.0 as $ty).powi(exp as i32) } } } }; } macro_rules! from_bytes { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { s.bytes().into() } } }; } macro_rules! from_str { ($ ty : ty) => { impl Parse for $ty { #[inline] fn parse(s: &mut I) -> Self { s.str().into() } } }; } macro_rules ! impls { ($ m : ident , $ ($ ty : ty) ,*) => { $ ($ m ! ($ ty) ;) * } ; } impls!(uint, usize, u8, u16, u32, u64, u128); impls!(int, isize, i8, i16, i32, i64, i128); impls!(float, f32, f64); impls!(from_bytes, Vec, Box<[u8]>); impls!(from_str, String); #[derive(Clone)] pub struct SplitWs { src: T, buf: Vec, pos: usize, len: usize, } const BUF_SIZE: usize = 1 << 26; impl SplitWs { pub fn new(src: T) -> Self { Self { src, buf: vec![0; BUF_SIZE], pos: 0, len: 0, } } #[inline(always)] fn peek(&self) -> &[u8] { unsafe { self.buf.get_unchecked(self.pos..self.len) } } #[inline(always)] fn consume(&mut self, n: usize) -> &[u8] { let pos = self.pos; self.pos += n; unsafe { self.buf.get_unchecked(pos..self.pos) } } fn read(&mut self) -> usize { self.buf.copy_within(self.pos..self.len, 0); self.len -= self.pos; self.pos = 0; if self.len == self.buf.len() { self.buf.resize(2 * self.buf.len(), 0); } loop { match self.src.read(&mut self.buf[self.len..]) { Ok(n) => { self.len += n; return n; } Err(e) if e.kind() == io::ErrorKind::WouldBlock => {} Err(e) => panic!("io error: {:?}", e), } } } } impl Input for SplitWs { #[inline] fn bytes(&mut self) -> &[u8] { loop { if let Some(del) = self.peek().iter().position(|c| c.is_ascii_whitespace()) { if del > 0 { let s = self.consume(del + 1); return s.split_last().unwrap().1; } else { self.consume(1); } } else if self.read() == 0 { return self.consume(self.len - self.pos); } } } } } 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] #[doc(hidden)] 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) ,*) => { if std :: env :: var ("ND") . map (| v | & v == "0") . unwrap_or (true) { eln ! (__tstr ! ($ ($ a) ,*) , file ! () , line ! () , $ (stringify ! ($ a) , $ a) ,*) ; } } ; } }