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)] 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) } // https://yukicoder.me/problems/no/1856 (3.5) // https://yukicoder.me/problems/no/2084 と制約だけが違う。 // 各 i について、長さ i で要素が [0, M] の数列の mex の和が求まれば良い。 // j <= M のとき、mex が j である数列の総数は (M)^i - C(j, 1)(M-1)^i + … + (-1)^j (M-j)^i である。 // これを 0 <= i <= N で重み C(N, i) M^(N-i) で合計すると \sum_{k <= j} (-1)^k jC(j, k) (2*M+1-k)^N である。 // mex が N 以下であることに注意すると  k も j も N 以下である。 // M+1 <= N のとき、j = M+1 のときの同じ値の合計は \sum_{k <= M+1} (-1)^k (M + 1) C(M+1, k) (2*M+2-k)^N である。 // Tags: combinatorics, binomial-expansion fn main() { let n: usize = get(); let m: i64 = get(); let (fac, invfac) = fact_init(n + 1); let mut tot = MInt::new(0); for j in 0..std::cmp::min(n, m as usize) + 1 { for k in 0..j + 1 { let tmp = fac[j] * invfac[j - k] * invfac[k] * MInt::new(2 * m + 1 - k as i64).pow(n as i64) * j as i64; if k % 2 == 0 { tot += tmp; } else { tot -= tmp; } } } if m + 1 <= n as i64 { let mm = m as usize; for k in 0..mm + 2 { let tmp = fac[mm + 1] * invfac[mm + 1 - k] * invfac[k] * MInt::new(2 * m + 2 - k as i64).pow(n as i64) * (m + 1) as i64; if k % 2 == 0 { tot += tmp; } else { tot -= tmp; } } } println!("{}", tot); }