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

; // C(a, b) fn comb(a: i64, b: i64) -> MInt { if a < 0 { return MInt::new(0); } let b = std::cmp::min(b, a - b); if b < 0 { return MInt::new(0); } let mut num = MInt::new(1); let mut den = MInt::new(1); for i in 1..b + 1 { num *= a + 1 - i; den *= i; } num * den.inv() } // \sum_{l <= i <= r} coef[j] i^j C(i, a) fn comb_poly_sum(rng: std::ops::RangeInclusive, a: i64, coef: &[MInt]) -> MInt { // Stirling numbers of second kind, with S2(n, k) negative for (n + k) % 2 != 0 // Complexity: O(n^2) // First terms are: // 1 // -1 1 // 1 -3 1 // -1 7 -6 1 let n = coef.len(); let mut stir = vec![vec![MInt::new(0); n + 1]; n + 1]; stir[0][0] += 1; for i in 1..n + 1 { for j in 1..i + 1 { let mut me = stir[i - 1][j - 1]; me -= stir[i - 1][j] * j as i64; stir[i][j] = me; } } let mut trans = vec![MInt::new(0); n]; for i in 0..n { for j in 0..i + 1 { trans[j] += stir[i + 1][j + 1] * coef[i]; } } let mut tot = MInt::new(0); let (l, r) = rng.into_inner(); let mut cur = MInt::new(1); // (a+1)...(a+i) for i in 0..n { tot += trans[i] * (comb(r + 1 + i as i64, a + i as i64 + 1) - comb(l + i as i64, a + i as i64 + 1)) * cur; cur *= a + i as i64 + 1; } tot } // https://yukicoder.me/problems/no/1989 (3) // 答えは N \sum_{0 <= i <= M} iC(2N-1 + M-i, 2N-1) である。 // N \sum_{2N-1 <= i <= 2N-1 +M} (2N-1+M-i) C(i, 2N-1) を計算すれば良い。 fn main() { let n: i64 = get(); let m: i64 = get(); println!("{}", comb_poly_sum(2 * n - 1..=2 * n - 1 + m, 2 * n - 1, &[MInt::new(2 * n - 1 + m), -MInt::new(1)]) * n); }