#899394 (Rust) No.2406 Difference of Coordinate Squared

• 問題: No.2406 Difference of Coordinate Squared
• ユーザー: koba-e964
• 提出日時: 2023-08-07 03:38:30
• 言語: Rust (1.77.0 + proconio)
• 結果: WA
• 実行時間: -
• コード長: 6,396 bytes
• コンパイル時間: 14,910 ms
• コンパイル使用メモリ: 378,920 KB
• 実行使用メモリ: 17,920 KB
• 最終ジャッジ日時: 2024-11-07 07:03:46
• 合計ジャッジ時間: 15,937 ms
• ジャッジサーバーID （参考情報）: judge3 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	5 ms; 5,248 KB
testcase_01	AC	35 ms; 17,536 KB
testcase_02	AC	37 ms; 17,920 KB
testcase_03	WA	-
testcase_04	AC	36 ms; 17,664 KB
testcase_05	AC	13 ms; 5,248 KB
testcase_06	AC	23 ms; 9,088 KB
testcase_07	AC	21 ms; 7,552 KB
testcase_08	AC	28 ms; 12,416 KB
testcase_09	AC	29 ms; 12,800 KB
testcase_10	AC	33 ms; 16,256 KB
testcase_11	AC	30 ms; 13,952 KB
testcase_12	AC	32 ms; 15,232 KB
testcase_13	AC	31 ms; 14,592 KB
testcase_14	AC	33 ms; 15,744 KB
testcase_15	AC	34 ms; 17,024 KB
testcase_16	AC	26 ms; 11,136 KB
testcase_17	AC	6 ms; 5,248 KB
testcase_18	WA	-
testcase_19	AC	33 ms; 15,488 KB
testcase_20	AC	34 ms; 16,640 KB
testcase_21	AC	25 ms; 10,240 KB
testcase_22	WA	-
testcase_23	AC	35 ms; 17,152 KB
testcase_24	AC	10 ms; 5,504 KB
testcase_25	WA	-
testcase_26	AC	13 ms; 5,248 KB
testcase_27	WA	-
testcase_28	AC	13 ms; 5,248 KB
testcase_29	AC	5 ms; 5,248 KB
testcase_30	AC	13 ms; 5,248 KB
testcase_31	AC	5 ms; 5,248 KB
testcase_32	AC	5 ms; 5,248 KB
testcase_33	AC	13 ms; 5,248 KB
testcase_34	AC	5 ms; 5,248 KB
testcase_35	AC	13 ms; 5,248 KB
testcase_36	AC	5 ms; 5,248 KB
testcase_37	AC	5 ms; 5,248 KB
testcase_38	AC	13 ms; 5,248 KB
testcase_39	WA	-
testcase_40	AC	12 ms; 5,248 KB
testcase_41	AC	13 ms; 5,248 KB
testcase_42	WA	-
testcase_43	AC	5 ms; 5,248 KB
testcase_44	AC	12 ms; 5,248 KB
testcase_45	AC	5 ms; 5,248 KB
testcase_46	AC	13 ms; 5,248 KB
testcase_47	AC	5 ms; 5,248 KB
testcase_48	WA	-
testcase_49	AC	5 ms; 5,248 KB
testcase_50	AC	5 ms; 5,248 KB
testcase_51	AC	13 ms; 5,248 KB
testcase_52	AC	12 ms; 5,248 KB
testcase_53	AC	13 ms; 5,248 KB
testcase_54	AC	13 ms; 5,248 KB
testcase_55	AC	5 ms; 5,248 KB
testcase_56	AC	1 ms; 5,248 KB

ソースコード

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<u8> = 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: std::str::FromStr>() -> 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<M> { pub x: i64, phantom: ::std::marker::PhantomData<M> }
    impl<M: Mod> ModInt<M> {
        // 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<M: Mod> Default for ModInt<M> {
        fn default() -> Self { Self::new_internal(0) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> Add<T> for ModInt<M> {
        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<M: Mod, T: Into<ModInt<M>>> Sub<T> for ModInt<M> {
        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<M: Mod, T: Into<ModInt<M>>> Mul<T> for ModInt<M> {
        type Output = Self;
        fn mul(self, other: T) -> Self { ModInt::new(self.x * other.into().x % M::m()) }
    }
    impl<M: Mod, T: Into<ModInt<M>>> AddAssign<T> for ModInt<M> {
        fn add_assign(&mut self, other: T) { *self = *self + other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> SubAssign<T> for ModInt<M> {
        fn sub_assign(&mut self, other: T) { *self = *self - other; }
    }
    impl<M: Mod, T: Into<ModInt<M>>> MulAssign<T> for ModInt<M> {
        fn mul_assign(&mut self, other: T) { *self = *self * other; }
    }
    impl<M: Mod> Neg for ModInt<M> {
        type Output = Self;
        fn neg(self) -> Self { ModInt::new(0) - self }
    }
    impl<M> ::std::fmt::Display for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            self.x.fmt(f)
        }
    }
    impl<M: Mod> ::std::fmt::Debug for ModInt<M> {
        fn fmt(&self, f: &mut ::std::fmt::Formatter) -> ::std::fmt::Result {
            let (mut a, mut b, _) = red(self.x, M::m());
            if b < 0 {
                a = -a;
                b = -b;
            }
            write!(f, "{}/{}", a, b)
        }
    }
    impl<M: Mod> From<i64> for ModInt<M> {
        fn from(x: i64) -> Self { Self::new(x) }
    }
    // Finds the simplest fraction x/y congruent to r mod p.
    // The return value (x, y, z) satisfies x = y * r + z * p.
    fn red(r: i64, p: i64) -> (i64, i64, i64) {
        if r.abs() <= 10000 {
            return (r, 1, 0);
        }
        let mut nxt_r = p % r;
        let mut q = p / r;
        if 2 * nxt_r >= r {
            nxt_r -= r;
            q += 1;
        }
        if 2 * nxt_r <= -r {
            nxt_r += r;
            q -= 1;
        }
        let (x, z, y) = red(nxt_r, r);
        (x, y - q * z, z)
    }
} // mod mod_int

macro_rules! define_mod {
    ($struct_name: ident, $modulo: expr) => {
        #[derive(Copy, Clone, PartialEq, Eq, PartialOrd, Ord, Hash)]
        pub 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<P>;

// Depends on MInt.rs
fn fact_init(w: usize) -> (Vec<MInt>, Vec<MInt>) {
    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)
}

fn calc(n: i64, a: i64, fac: &[MInt], invfac: &[MInt]) -> MInt {
    if a.abs() > n || (n + a) % 2 != 0 {
        return 0.into();
    }
    let n = n as usize;
    let a = a.abs() as usize;
    fac[n] * invfac[(n + a) / 2] * invfac[(n - a) / 2]
}

// https://yukicoder.me/problems/no/2406 (3.5)
// a = x + y, b = x - y とすると、操作では a や b が**独立に** 1 増えたり減ったりする。
// x^2 - y^2 = ab = M となる a, b それぞれに対して確率を求めれば良い。
// その確率は f(a, N)f(b, N) である。
// ここで f(s, N) = |s| <= N && (s + N) % 2 == 0 ? C(N, (N-s)/2)/2^N : 0 である。
// -> WA。 M = 0 のときの a, b の列挙に問題があった。
fn main() {
    let n: i64 = get();
    let m: i64 = get();
    let (fac, invfac) = fact_init(n as usize + 1);
    let p2 = MInt::new(2).inv().pow(n as i64);
    if m == 0 {
        let mut ans = MInt::new(0);
        let tmp = calc(n, 0, &fac, &invfac);
        ans += tmp * 2 - tmp * tmp;
        println!("{}", ans * p2 * p2);
        return;
    }
    let mut pairs = vec![];
    for d in 1..1_000_001 {
        if m % d == 0 {
            pairs.push((d, m / d));
            pairs.push((m / d, d));
            pairs.push((-d, -m / d));
            pairs.push((-m / d, -d));
        }
    }
    pairs.sort(); pairs.dedup();
    let mut ans = MInt::new(0);
    for (a, b) in pairs {
        ans += calc(n, a, &fac, &invfac) * calc(n, b, &fac, &invfac) * p2 * p2;
    }
    println!("{}", ans);
}