#![allow(unused_imports)] #![allow(non_snake_case, unused)] use std::cmp::*; use std::collections::*; use std::ops::*; // https://atcoder.jp/contests/hokudai-hitachi2019-1/submissions/10518254 macro_rules! eprint { ($($t:tt)*) => {{ use ::std::io::Write; let _ = write!(::std::io::stderr(), $($t)*); }}; } macro_rules! eprintln { () => { eprintln!(""); }; ($($t:tt)*) => {{ use ::std::io::Write; let _ = writeln!(::std::io::stderr(), $($t)*); }}; } macro_rules! dbg { ($v:expr) => {{ let val = $v; eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val); val }} } macro_rules! mat { ($($e:expr),*) => { Vec::from(vec![$($e),*]) }; ($($e:expr,)*) => { Vec::from(vec![$($e),*]) }; ($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) }; ($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) }; } macro_rules! ok { ($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => { $a$([$i])*.$f($($t),*) }; ($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { { let t = $e; ok!($a$([$i])*.$f($($es),*)$(@$t)*@t) } }; } pub fn readln() -> String { let mut line = String::new(); ::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e)); line } macro_rules! read { ($($t:tt),*; $n:expr) => {{ let stdin = ::std::io::stdin(); let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| { let line = line.unwrap(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }).collect::>(); ret }}; ($($t:tt),*) => {{ let line = readln(); let mut it = line.split_whitespace(); _read!(it; $($t),*) }}; } macro_rules! _read { ($it:ident; [char]) => { _read!($it; String).chars().collect::>() }; ($it:ident; [u8]) => { Vec::from(_read!($it; String).into_bytes()) }; ($it:ident; usize1) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::().unwrap_or_else(|e| panic!("{}", e)) - 1 }; ($it:ident; [usize1]) => { $it.map(|s| s.parse::().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::>() }; ($it:ident; [$t:ty]) => { $it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::>() }; ($it:ident; $t:ty) => { $it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e)) }; ($it:ident; $($t:tt),+) => { ($(_read!($it; $t)),*) }; } pub fn main() { let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join(); } const MOD: usize = 998244353; const INF: i64 = std::i64::MAX/2; use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign}; type Num = usize; #[derive(Clone, Copy, Debug)] pub struct ModInt(pub T); impl Add> for ModInt { type Output = ModInt; fn add(self, rhs: ModInt) -> ModInt { self + rhs.0 } } impl Add for ModInt { type Output = ModInt; fn add(self, rhs: Num) -> ModInt { let mut t = rhs + self.0; if t >= MOD { t = t - MOD; } ModInt(t) } } impl Sub for ModInt { type Output = ModInt; fn sub(self, rhs: Num) -> ModInt { let rhs = if rhs >= MOD { rhs % MOD } else { rhs }; let value = if self.0 < rhs { self.0 + MOD } else { self.0 }; ModInt(value - rhs) } } impl Sub> for ModInt { type Output = ModInt; fn sub(self, rhs: ModInt) -> ModInt { self - rhs.0 } } impl AddAssign for ModInt { fn add_assign(&mut self, other: Num) { *self = *self + other; } } impl AddAssign> for ModInt { fn add_assign(&mut self, other: ModInt) { *self = *self + other; } } impl SubAssign for ModInt { fn sub_assign(&mut self, other: Num) { *self = *self - other; } } impl SubAssign> for ModInt { fn sub_assign(&mut self, other: ModInt) { *self = *self - other; } } impl Div for ModInt { type Output = ModInt; fn div(self, rhs: Num) -> ModInt { self * ModInt(rhs).pow(MOD - 2) } } impl Div> for ModInt { type Output = ModInt; fn div(self, rhs: ModInt) -> ModInt { self / rhs.0 } } impl DivAssign for ModInt { fn div_assign(&mut self, rhs: Num) { *self = *self / rhs } } impl DivAssign> for ModInt { fn div_assign(&mut self, rhs: ModInt) { *self = *self / rhs } } impl Mul> for ModInt { type Output = ModInt; fn mul(self, rhs: ModInt) -> ModInt { self * rhs.0 } } impl Mul for ModInt { type Output = ModInt; fn mul(self, rhs: Num) -> ModInt { let t = (self.0 * rhs) % MOD; ModInt(t) } } impl MulAssign for ModInt { fn mul_assign(&mut self, rhs: Num) { *self = *self * rhs; } } impl MulAssign> for ModInt { fn mul_assign(&mut self, rhs: ModInt) { *self = *self * rhs; } } impl ModInt { pub fn pow(self, e: usize) -> ModInt { let mut result = ModInt(1); let mut cur = self; let mut e = e; while e > 0 { if e & 1 == 1 { result *= cur; } e >>= 1; cur *= cur; } result } } pub struct Comb { fact: Vec>, factinv: Vec>, } impl Comb { /// Create a object that provides effiecint computation of combinations /// for input smaller than `n`. /// /// This requires `O(n)` time. pub fn new(n: usize) -> Comb { let mut fact: Vec> = vec![ModInt(0); n + 1]; let mut factinv: Vec> = vec![ModInt(0); n + 1]; fact[0] = ModInt(1); for i in 0..n { fact[i + 1] = fact[i] * (i + 1); } factinv[n] = fact[n].pow(MOD-2); for i in (0..n).rev() { factinv[i] = factinv[i + 1] * (i + 1); } Comb { fact: fact, factinv: factinv, } } /// `n! = 1 * 2 * ... * n` /// /// `O(1)` if n is smaller than input in `new` method. pub fn fact(&self, n: usize) -> ModInt { if let Some(x) = self.fact.get(n as usize) { *x } else if n >= MOD { ModInt(0) } else { // Note that this is slow if `n` is large. // Precalculation is a possible solution but doesn't work for any module number. let mut res = ModInt(1); for a in 1..(n + 1) { res *= a; } res } } /// returns `y` such that `n! * y == 1`. /// /// `O(1)` if n is smaller than input in `new` method. pub fn factinv(&self, n: usize) -> ModInt { if let Some(x) = self.factinv.get(n) { *x } else { self.fact(n).pow(MOD-2) } } /// `nPr = n! / (n - r)!` /// /// `O(1)` if n and r are smaller than input in `new` method. pub fn perm(&self, n: usize, r: usize) -> ModInt { if n >= r { self.fact(n) * self.factinv(n - r) } else { ModInt(0) } } /// `nCr = n! / (n - r)! / r!`. /// /// `O(1)` if n and r are smaller than input in `new` method. pub fn comb(&self, n: usize, r: usize) -> ModInt { let m = MOD; if n >= m { self.comb(n % m, r % m) * self.comb(n / m, r / m) // Lucas' theorem } else if n >= r { self.fact(n) * self.factinv(n - r) * self.factinv(r) } else { ModInt(0) } } } fn solve() { let (n,m,a,b) = read!(i64,i64,i64,i64); let t = a*(n-1)+1; let res = m-t; let mut ans = ModInt(0); let mut cum = vec![ModInt(0);m as usize+2]; let mut comb = Comb::new(n as usize - 1); for i in 0..(m+1) as usize { cum[i+1] = cum[i] + comb.comb(n as usize-1+i-1,i); } for i in 0..=res{ let x = min(res-i,b-t+1); if x<0 { continue; } ans += cum[x as usize + 1]; } ans *= comb.fact(n as usize); println!("{}",ans.0); } fn run() { solve(); }