#704344 (Rust) No.1145 Sums of Powers

• 問題: No.1145 Sums of Powers
• ユーザー: koba-e964
• 提出日時: 2021-10-02 20:42:33
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 764 ms / 2,000 ms
• コード長: 12,092 bytes
• コンパイル時間: 16,910 ms
• コンパイル使用メモリ: 378,004 KB
• 実行使用メモリ: 17,620 KB
• 最終ジャッジ日時: 2024-07-20 15:38:03
• 合計ジャッジ時間: 17,736 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

ファイルパターン	結果
other	AC * 6

ソースコード

#[allow(unused_imports)]
use std::cmp::*;
#[allow(unused_imports)]
use std::collections::*;
use std::io::{Write, BufWriter};
// 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:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($next, $t)).collect::<Vec<_>>()
    };
    ($next:expr, $t:ty) => ($next().parse::<$t>().expect("Parse error"));
}

/// 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, 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)]
        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>;

// FFT (in-place, verified as NTT only)
// R: Ring + Copy
// Verified by: https://judge.yosupo.jp/submission/53831
// Adopts the technique used in https://judge.yosupo.jp/submission/3153.
mod fft {
    use std::ops::*;
    // n should be a power of 2. zeta is a primitive n-th root of unity.
    // one is unity
    // Note that the result is bit-reversed.
    pub fn fft<R>(f: &mut [R], zeta: R, one: R)
        where R: Copy +
        Add<Output = R> +
        Sub<Output = R> +
        Mul<Output = R> {
        let n = f.len();
        assert!(n.is_power_of_two());
        let mut m = n;
        let mut base = zeta;
        unsafe {
            while m > 2 {
                m >>= 1;
                let mut r = 0;
                while r < n {
                    let mut w = one;
                    for s in r..r + m {
                        let &u = f.get_unchecked(s);
                        let d = *f.get_unchecked(s + m);
                        *f.get_unchecked_mut(s) = u + d;
                        *f.get_unchecked_mut(s + m) = w * (u - d);
                        w = w * base;
                    }
                    r += 2 * m;
                }
                base = base * base;
            }
            if m > 1 {
                // m = 1
                let mut r = 0;
                while r < n {
                    let &u = f.get_unchecked(r);
                    let d = *f.get_unchecked(r + 1);
                    *f.get_unchecked_mut(r) = u + d;
                    *f.get_unchecked_mut(r + 1) = u - d;
                    r += 2;
                }
            }
        }
    }
    pub fn inv_fft<R>(f: &mut [R], zeta_inv: R, one: R)
        where R: Copy +
        Add<Output = R> +
        Sub<Output = R> +
        Mul<Output = R> {
        let n = f.len();
        assert!(n.is_power_of_two());
        let zeta = zeta_inv; // inverse FFT
        let mut zetapow = Vec::with_capacity(20);
        {
            let mut m = 1;
            let mut cur = zeta;
            while m < n {
                zetapow.push(cur);
                cur = cur * cur;
                m *= 2;
            }
        }
        let mut m = 1;
        unsafe {
            if m < n {
                zetapow.pop();
                let mut r = 0;
                while r < n {
                    let &u = f.get_unchecked(r);
                    let d = *f.get_unchecked(r + 1);
                    *f.get_unchecked_mut(r) = u + d;
                    *f.get_unchecked_mut(r + 1) = u - d;
                    r += 2;
                }
                m = 2;
            }
            while m < n {
                let base = zetapow.pop().unwrap();
                let mut r = 0;
                while r < n {
                    let mut w = one;
                    for s in r..r + m {
                        let &u = f.get_unchecked(s);
                        let d = *f.get_unchecked(s + m) * w;
                        *f.get_unchecked_mut(s) = u + d;
                        *f.get_unchecked_mut(s + m) = u - d;
                        w = w * base;
                    }
                    r += 2 * m;
                }
                m *= 2;
            }
        }
    }
}

// Depends on: fft.rs, MInt.rs
// Primitive root defaults to 3 (for 998244353); for other moduli change the value of it.
fn conv(a: Vec<MInt>, b: Vec<MInt>) -> Vec<MInt> {
    let n = a.len() - 1;
    let m = b.len() - 1;
    let mut p = 1;
    while p <= n + m { p *= 2; }
    let mut f = vec![MInt::new(0); p];
    let mut g = vec![MInt::new(0); p];
    for i in 0..n + 1 { f[i] = a[i]; }
    for i in 0..m + 1 { g[i] = b[i]; }
    let fac = MInt::new(p as i64).inv();
    let zeta = MInt::new(3).pow((MOD - 1) / p as i64);
    fft::fft(&mut f, zeta, 1.into());
    fft::fft(&mut g, zeta, 1.into());
    for i in 0..p { f[i] *= g[i] * fac; }
    fft::inv_fft(&mut f, zeta.inv(), 1.into());
    f[..n + m + 1].to_vec()
}

// Computes f^{-1} mod x^{f.len()}.
// Reference: https://codeforces.com/blog/entry/56422
// Complexity: O(n log n)
// Verified by: https://judge.yosupo.jp/submission/3219
// Depends on: MInt.rs, fft.rs
fn fps_inv<P: mod_int::Mod + PartialEq>(
    f: &[mod_int::ModInt<P>],
    gen: mod_int::ModInt<P>
) -> Vec<mod_int::ModInt<P>> {
    let n = f.len();
    assert!(n.is_power_of_two());
    assert_eq!(f[0], 1.into());
    let mut sz = 1;
    let mut r = vec![mod_int::ModInt::new(0); n];
    let mut tmp_f = vec![mod_int::ModInt::new(0); n];
    let mut tmp_r = vec![mod_int::ModInt::new(0); n];
    r[0] = 1.into();
    // Adopts the technique used in https://judge.yosupo.jp/submission/3153
    while sz < n {
        let zeta = gen.pow((P::m() - 1) / sz as i64 / 2);
        tmp_f[..2 * sz].copy_from_slice(&f[..2 * sz]);
        tmp_r[..2 * sz].copy_from_slice(&r[..2 * sz]);
        fft::fft(&mut tmp_r[..2 * sz], zeta, 1.into());
        fft::fft(&mut tmp_f[..2 * sz], zeta, 1.into());
        let fac = mod_int::ModInt::new(2 * sz as i64).inv().pow(2);
        for i in 0..2 * sz {
            tmp_f[i] *= tmp_r[i];
        }
        fft::inv_fft(&mut tmp_f[..2 * sz], zeta.inv(), 1.into());
        for v in &mut tmp_f[..sz] {
            *v = 0.into();
        }
        fft::fft(&mut tmp_f[..2 * sz], zeta, 1.into());
        for i in 0..2 * sz {
            tmp_f[i] = -tmp_f[i] * tmp_r[i] * fac;
        }
        fft::inv_fft(&mut tmp_f[..2 * sz], zeta.inv(), 1.into());
        r[sz..2 * sz].copy_from_slice(&tmp_f[sz..2 * sz]);
        sz *= 2;
    }
    r
}

fn dfs(polys: &[Vec<MInt>]) -> (Vec<MInt>, Vec<MInt>) {
    let len = polys.len();
    if len == 0 {
        return (vec![MInt::new(0)], vec![MInt::new(1)]);
    }
    if len == 1 {
        return (vec![MInt::new(1)], polys[0].to_vec());
    }
    let mid = len / 2;
    let (n0, d0) = dfs(&polys[..mid]);
    let (n1, d1) = dfs(&polys[mid..]);
    let mut n = conv(n0, d1.clone());
    {
        let sub = conv(n1, d0.clone());
        let to = max(n.len(), sub.len());
        n.resize(to, 0.into());
        for i in 0..sub.len() {
            n[i] += sub[i];
        }
    }
    let d = conv(d0, d1);
    (n, d)
}

// Tags: binary-splitting, fps
fn main() {
    // In order to avoid potential stack overflow, spawn a new thread.
    let stack_size = 104_857_600; // 100 MB
    let thd = std::thread::Builder::new().stack_size(stack_size);
    thd.spawn(|| solve()).unwrap().join().unwrap();
}

fn solve() {
    let out = std::io::stdout();
    let mut out = BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    #[allow(unused)]
    macro_rules! putvec {
        ($v:expr) => {
            for i in 0..$v.len() {
                puts!("{}{}", $v[i], if i + 1 == $v.len() {"\n"} else {" "});
            }
        }
    }
    input! {
        n: usize, m: usize,
        a: [i64; n],
    }
    let mut polys = vec![vec![MInt::new(1), MInt::new(0)]; n];
    for i in 0..n {
        polys[i][1] = -MInt::new(a[i]);
    }
    let (num, mut den) = dfs(&polys);
    let mut p = 1;
    while p < max(m + 1, den.len()) {
        p *= 2;
    }
    den.resize(p, 0.into());
    let invden = fps_inv(&den, 3.into());
    let res = conv(num, invden);
    putvec!(res[1..m + 1]);
}