// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes.by_ref().map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr,) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error")); } const MOD: i64 = 998_244_353; // https://yukicoder.me/problems/no/1771 (3) // https://yukicoder.me/problems/no/1772 (3.5) // 4000^2 が許される。以下の 5 種類の遷移に分けて DP: // 1. “” (if x == y) // 2. “AB” + ?? (x-1, y) // 3. “BA” + ?? (x, y-1) // 4. “AA” + ?? (x-1, y-1) // 5. “BB” + ?? (x-1, y-1) fn main() { input!(x: usize, y: usize); assert!(x <= 4000 && y <= 4000); let mut dp = vec![vec![0; y + 1]; x + 1]; dp[0][0] = 1; for i in 0..x + 1 { for j in 0..y + 1 { if i + j == 0 { continue; } let mut me = 0; if i == j { me += 1; } if i > 0 { me += dp[i - 1][j]; } if j > 0 { me += dp[i][j - 1]; } if i > 0 && j > 0 { me += 2 * dp[i - 1][j - 1]; } dp[i][j] = me % MOD; } } println!("{}", dp[x][y]); }