#523183 (Rust) No.1145 Sums of Powers

• 問題: No.1145 Sums of Powers
• ユーザー: akakimidori
• 提出日時: 2020-08-01 16:26:27
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 696 ms / 2,000 ms
• コード長: 21,196 bytes
• コンパイル時間: 12,700 ms
• コンパイル使用メモリ: 384,272 KB
• 実行使用メモリ: 19,020 KB
• 最終ジャッジ日時: 2024-07-08 02:49:12
• 合計ジャッジ時間: 16,205 ms
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
other	AC * 6

ソースコード

// ---------- begin ModInt ----------
mod modint {

    #[allow(dead_code)]
    pub struct Mod;
    impl ConstantModulo for Mod {
        const MOD: u32 = 1_000_000_007;
    }

    #[allow(dead_code)]
    pub struct StaticMod;
    static mut STATIC_MOD: u32 = 0;
    impl Modulo for StaticMod {
        fn modulo() -> u32 {
            unsafe { STATIC_MOD }
        }
    }

    #[allow(dead_code)]
    impl StaticMod {
        pub fn set_modulo(p: u32) {
            unsafe {
                STATIC_MOD = p;
            }
        }
    }

    use std::marker::*;
    use std::ops::*;

    pub trait Modulo {
        fn modulo() -> u32;
    }

    pub trait ConstantModulo {
        const MOD: u32;
    }

    impl<T> Modulo for T
    where
        T: ConstantModulo,
    {
        fn modulo() -> u32 {
            T::MOD
        }
    }

    pub struct ModInt<T>(pub u32, PhantomData<T>);

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::new_unchecked(self.0)
        }
    }

    impl<T> Copy for ModInt<T> {}

    impl<T: Modulo> Add for ModInt<T> {
        type Output = ModInt<T>;
        fn add(self, rhs: Self) -> Self::Output {
            let mut d = self.0 + rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> AddAssign for ModInt<T> {
        fn add_assign(&mut self, rhs: Self) {
            *self = *self + rhs;
        }
    }

    impl<T: Modulo> Sub for ModInt<T> {
        type Output = ModInt<T>;
        fn sub(self, rhs: Self) -> Self::Output {
            let mut d = T::modulo() + self.0 - rhs.0;
            if d >= T::modulo() {
                d -= T::modulo();
            }
            ModInt::new_unchecked(d)
        }
    }

    impl<T: Modulo> SubAssign for ModInt<T> {
        fn sub_assign(&mut self, rhs: Self) {
            *self = *self - rhs;
        }
    }

    impl<T: Modulo> Mul for ModInt<T> {
        type Output = ModInt<T>;
        fn mul(self, rhs: Self) -> Self::Output {
            let v = self.0 as u64 * rhs.0 as u64 % T::modulo() as u64;
            ModInt::new_unchecked(v as u32)
        }
    }

    impl<T: Modulo> MulAssign for ModInt<T> {
        fn mul_assign(&mut self, rhs: Self) {
            *self = *self * rhs;
        }
    }

    impl<T: Modulo> Neg for ModInt<T> {
        type Output = ModInt<T>;
        fn neg(self) -> Self::Output {
            if self.0 == 0 {
                Self::zero()
            } else {
                Self::new_unchecked(T::modulo() - self.0)
            }
        }
    }

    impl<T> std::fmt::Display for ModInt<T> {
        fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
            write!(f, "{}", self.0)
        }
    }

    impl<T: Modulo> std::str::FromStr for ModInt<T> {
        type Err = std::num::ParseIntError;
        fn from_str(s: &str) -> Result<Self, Self::Err> {
            let val = s.parse::<u32>()?;
            Ok(ModInt::new(val))
        }
    }

    impl<T: Modulo> From<usize> for ModInt<T> {
        fn from(val: usize) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as usize) as u32)
        }
    }

    impl<T: Modulo> From<i64> for ModInt<T> {
        fn from(val: i64) -> ModInt<T> {
            let m = T::modulo() as i64;
            ModInt::new((val % m + m) as u32)
        }
    }

    #[allow(dead_code)]
    impl<T> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            ModInt(d, PhantomData)
        }
        pub fn zero() -> Self {
            ModInt::new_unchecked(0)
        }
        pub fn one() -> Self {
            ModInt::new_unchecked(1)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModInt<T> {
        pub fn new(d: u32) -> Self {
            ModInt::new_unchecked(d % T::modulo())
        }
        pub fn pow(&self, mut n: u64) -> Self {
            let mut t = Self::one();
            let mut s = *self;
            while n > 0 {
                if n & 1 == 1 {
                    t *= s;
                }
                s *= s;
                n >>= 1;
            }
            t
        }
        pub fn inv(&self) -> Self {
            assert!(self.0 != 0);
            self.pow(T::modulo() as u64 - 2)
        }
    }

    #[allow(dead_code)]
    pub fn mod_pow(r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        let mut s = r % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s % m;
            }
            s = s * s % m;
            n >>= 1;
        }
        t
    }
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
mod precalc {
    use super::modint::*;
    #[allow(dead_code)]
    pub struct Precalc<T> {
        inv: Vec<ModInt<T>>,
        fact: Vec<ModInt<T>>,
        ifact: Vec<ModInt<T>>,
    }
    #[allow(dead_code)]
    impl<T: Modulo> Precalc<T> {
        pub fn new(n: usize) -> Precalc<T> {
            let mut inv = vec![ModInt::one(); n + 1];
            let mut fact = vec![ModInt::one(); n + 1];
            let mut ifact = vec![ModInt::one(); n + 1];
            for i in 2..(n + 1) {
                fact[i] = fact[i - 1] * ModInt::new_unchecked(i as u32);
            }
            ifact[n] = fact[n].inv();
            if n > 0 {
                inv[n] = ifact[n] * fact[n - 1];
            }
            for i in (1..n).rev() {
                ifact[i] = ifact[i + 1] * ModInt::new_unchecked((i + 1) as u32);
                inv[i] = ifact[i] * fact[i - 1];
            }
            Precalc {
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        pub fn inv(&self, n: usize) -> ModInt<T> {
            assert!(n > 0);
            self.inv[n]
        }
        pub fn fact(&self, n: usize) -> ModInt<T> {
            self.fact[n]
        }
        pub fn ifact(&self, n: usize) -> ModInt<T> {
            self.ifact[n]
        }
        pub fn perm(&self, n: usize, k: usize) -> ModInt<T> {
            if k > n {
                return ModInt::zero();
            }
            self.fact[n] * self.ifact[n - k]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModInt<T> {
            if k > n {
                return ModInt::zero();
            }
            self.fact[n] * self.ifact[k] * self.ifact[n - k]
        }
    }
}
// ---------- end Precalc ----------
// ---------- begin NTT ----------
#[allow(dead_code)]
mod transform {
    use super::modint::*;
    pub trait NTTFriendly: ConstantModulo {
        fn order() -> usize;
        fn zeta() -> u32;
    }
    pub fn ntt<T: NTTFriendly>(f: &mut [ModInt<T>]) {
        let n = f.len();
        assert!(n.count_ones() == 1);
        assert!(n <= T::order());
        let len = n.trailing_zeros() as usize;
        let mut zeta = Vec::with_capacity(len);
        let mut r = ModInt::new_unchecked(T::zeta()).pow((T::order() >> len) as u64);
        for _ in 0..len {
            zeta.push(r);
            r = r * r;
        }
        for (k, &z) in zeta.iter().rev().enumerate().rev() {
            let m = 1 << k;
            for f in f.chunks_exact_mut(2 * m) {
                let mut q = ModInt::one();
                let (x, y) = f.split_at_mut(m);
                for (x, y) in x.iter_mut().zip(y.iter_mut()) {
                    let a = *x;
                    let b = *y;
                    *x = a + b;
                    *y = (a - b) * q;
                    q *= z;
                }
            }
        }
    }
    pub fn intt<T: NTTFriendly>(f: &mut [ModInt<T>]) {
        let n = f.len();
        assert!(n.count_ones() == 1);
        assert!(n <= T::order());
        let len = n.trailing_zeros() as usize;
        let mut zeta = Vec::with_capacity(len);
        let mut r = ModInt::new_unchecked(T::zeta()).inv().pow((T::order() >> len) as u64);
        for _ in 0..len {
            zeta.push(r);
            r = r * r;
        }
        for (k, &z) in zeta.iter().rev().enumerate() {
            let m = 1 << k;
            for f in f.chunks_exact_mut(2 * m) {
                let mut q = ModInt::one();
                let (x, y) = f.split_at_mut(m);
                for (x, y) in x.iter_mut().zip(y.iter_mut()) {
                    let a = *x;
                    let b = *y * q;
                    *x = a + b;
                    *y = a - b;
                    q *= z;
                }
            }
        }
        let ik = ModInt::new_unchecked((T::MOD + 1) >> 1).pow(len as u64);
        for f in f.iter_mut() {
            *f *= ik;
        }
    }
    pub fn multiply<T: NTTFriendly>(a: &[ModInt<T>], b: &[ModInt<T>]) -> Vec<ModInt<T>> {
        if a.is_empty() || b.is_empty() {
            return vec![];
        }
        let n = a.len() + b.len() - 1;
        let k = n.next_power_of_two();
        assert!(k <= T::order());
        let mut f = Vec::with_capacity(k);
        let mut g = Vec::with_capacity(k);
        f.extend_from_slice(a);
        f.resize(k, ModInt::zero());
        ntt(&mut f);
        g.extend_from_slice(b);
        g.resize(k, ModInt::zero());
        ntt(&mut g);
        for (f, g) in f.iter_mut().zip(g.iter()) {
            *f *= *g;
        }
        intt(&mut f);
        f.truncate(n);
        f
    }
}
// ---------- end NTT ----------
// ---------- begin polynomial ----------
#[allow(dead_code)]
mod poly {
    use super::modint::*;
    use super::transform;
    pub struct Polynomial<T> {
        pub a: Vec<ModInt<T>>,
    }
    impl<T: Modulo> Clone for Polynomial<T> {
        fn clone(&self) -> Self {
            Polynomial::new(self.a.iter().map(|a| a.clone()).collect())
        }
    }
    impl<T: Modulo> Polynomial<T> {
        pub fn new(a: Vec<ModInt<T>>) -> Self {
            let mut a = Polynomial { a: a };
            a.fix();
            a
        }
        pub fn from_slice(a: &[ModInt<T>]) -> Self {
            let mut b = Vec::with_capacity(a.len());
            b.extend_from_slice(a);
            Self::new(b)
        }
        pub fn zero() -> Self {
            Polynomial::new(vec![])
        }
        pub fn one() -> Self {
            Polynomial::new(vec![ModInt::one()])
        }
        pub fn get(&self, x: usize) -> ModInt<T> {
            self.a.get(x).cloned().unwrap_or(ModInt::zero())
        }
        pub fn len(&self) -> usize {
            self.a.len()
        }
        pub fn reverse(&self, n: usize) -> Self {
            assert!(self.len() >= n);
            let mut a = Vec::with_capacity(n);
            a.extend_from_slice(&self.a);
            a.resize(n, ModInt::zero());
            a.reverse();
            Self::new(a)
        }
        pub fn truncate(&self, n: usize) -> Self {
            let mut b = self.a.clone();
            b.truncate(n);
            Polynomial::new(b)
        }
        pub fn eval(&self, x: ModInt<T>) -> ModInt<T> {
            let mut ans = ModInt::zero();
            for a in self.a.iter().rev() {
                ans = ans * x + *a;
            }
            ans
        }
        pub fn fix(&mut self) {
            while self.a.last().map_or(false, |a| a.is_zero()) {
                self.a.pop();
            }
        }
        pub fn derivative(&self) -> Self {
            if self.len() < 2 {
                return Polynomial::zero();
            }
            let mut b = vec![ModInt::zero(); self.len() - 1];
            for (i, (b, a)) in b.iter_mut().zip(self.a.iter().skip(1)).enumerate() {
                *b = *a * ModInt::from(i + 1);
            }
            Polynomial::new(b)
        }
        pub fn integral(&self) -> Self {
            if self.len() < 1 {
                return Polynomial::zero();
            }
            let mut b = vec![ModInt::zero(); self.len() + 1];
            let mut inv = vec![ModInt::one(); self.len() + 1];
            b[1] = self.a[0];
            for (i, (b, a)) in b[1..].iter_mut().zip(self.a.iter()).enumerate().skip(1) {
                let k = i + 1;
                inv[k] = -inv[T::modulo() as usize % k] * ModInt::from(T::modulo() as usize / k);
                *b = *a * inv[k];
            }
            Polynomial::new(b)
        }
        pub fn add(&self, rhs: &Self) -> Self {
            let mut ans = vec![ModInt::zero(); std::cmp::max(self.a.len(), rhs.a.len())];
            for (ans, a) in ans.iter_mut().zip(self.a.iter()) {
                *ans = *a;
            }
            for (ans, a) in ans.iter_mut().zip(rhs.a.iter()) {
                *ans += *a;
            }
            Polynomial::new(ans)
        }
        pub fn add_assign(&mut self, rhs: &Self) {
            if self.len() < rhs.len() {
                self.a.resize(rhs.len(), ModInt::zero());
            }
            for (a, b) in self.a.iter_mut().zip(rhs.a.iter()) {
                *a += *b;
            }
        }
        pub fn sub(&self, rhs: &Self) -> Self {
            let mut ans = vec![ModInt::zero(); std::cmp::max(self.a.len(), rhs.a.len())];
            for (ans, a) in ans.iter_mut().zip(self.a.iter()) {
                *ans = *a;
            }
            for (ans, a) in ans.iter_mut().zip(rhs.a.iter()) {
                *ans -= *a;
            }
            Polynomial::new(ans)
        }
        pub fn sub_assign(&mut self, rhs: &Self) {
            if self.len() < rhs.len() {
                self.a.resize(rhs.len(), ModInt::zero());
            }
            for (a, b) in self.a.iter_mut().zip(rhs.a.iter()) {
                *a -= *b;
            }
        }
    }
    impl<T: transform::NTTFriendly> Polynomial<T> {
        pub fn mul(&self, rhs: &Self) -> Self {
            Self::new(transform::multiply(&self.a, &rhs.a))
        }
        pub fn inverse(&self, n: usize) -> Self {
            assert!(self.a.len() > 0 && self.a[0].0 > 0);
            let len = n.next_power_of_two();
            assert!(2 * len <= T::order());
            let mut b = Vec::with_capacity(len);
            b.push(self.a[0].inv());
            let mut f = Vec::with_capacity(2 * len);
            let mut g = Vec::with_capacity(2 * len);
            let mut size = 1;
            while b.len() < n {
                size <<= 1;
                f.clear();
                f.extend_from_slice(&b);
                f.resize(2 * size, ModInt::zero());
                g.clear();
                if self.a.len() >= size {
                    g.extend_from_slice(&self.a[..size]);
                } else {
                    g.extend_from_slice(&self.a);
                }
                g.resize(2 * size, ModInt::zero());
                transform::ntt(&mut f);
                transform::ntt(&mut g);
                for (g, f) in g.iter_mut().zip(f.iter()) {
                    *g *= *f * *f;
                }
                transform::intt(&mut g);
                b.resize(size, ModInt::zero());
                for (b, g) in b.iter_mut().zip(g.iter()) {
                    *b = *b + *b - *g;
                }
            }
            b.truncate(n);
            Polynomial::new(b)
        }
        pub fn div_rem(&self, rhs: &Self) -> (Self, Self) {
            let n = self.len();
            let m = rhs.len();
            assert!(m > 0);
            if n < m {
                return (Polynomial::zero(), self.clone());
            }
            let ia = self.reverse(n).truncate(n - m + 1);
            let ib = rhs.reverse(m).inverse(n - m + 1);
            let id = ia.mul(&ib).truncate(n - m + 1);
            let div = id.reverse(n - m + 1);
            let rem = self.sub(&rhs.mul(&div)).truncate(m - 1);
            (div, rem)
        }
        pub fn rem(&self, rhs: &Self) -> Self {
            self.div_rem(rhs).1
        }
        pub fn log(&self, n: usize) -> Self {
            assert!(self.len() > 0 && self.a[0].0 == 1);
            self.derivative()
                .mul(&self.inverse(n))
                .truncate(n - 1)
                .integral()
        }
        pub fn exp(&self, n: usize) -> Self {
            assert!(self.a.get(0).map_or(true, |a| a.is_zero()) && n <= T::order());
            let mut b = Polynomial::new(vec![ModInt::one()]);
            let mut size = 1;
            while size < n {
                size <<= 1;
                let f = b.log(size);
                let f = Polynomial::from_slice(&self.a[..std::cmp::min(self.len(), size)]).sub(&f);
                b = b.add(&b.mul(&f)).truncate(size);
            }
            b.truncate(n)
        }
        pub fn multi_eval(&self, x: &[ModInt<T>]) -> Vec<ModInt<T>> {
            let size = x.len().next_power_of_two();
            let mut seg = vec![Some(Polynomial::one()); 2 * size];
            for (seg, x) in seg[size..].iter_mut().zip(x.iter()) {
                *seg = Some(Polynomial::from_slice(&[-*x, ModInt::one()]));
            }
            for i in (1..size).rev() {
                seg[i] = Some(
                    seg[2 * i]
                        .as_ref()
                        .unwrap()
                        .mul(seg[2 * i + 1].as_ref().unwrap()),
                );
            }
            let mut rem = vec![None; 2 * size];
            rem[1] = Some(self.rem(&seg[1].take().unwrap()));
            for i in 1..size {
                let a = rem[i].take().unwrap();
                rem[2 * i] = Some(a.rem(&seg[2 * i].take().unwrap()));
                rem[2 * i + 1] = Some(a.rem(&seg[2 * i + 1].take().unwrap()));
            }
            let mut ans = Vec::with_capacity(x.len());
            for a in rem[size..].iter_mut().take(x.len()) {
                ans.push(a.take().unwrap().get(0));
            }
            ans
        }
        pub fn interpolation(x: &[ModInt<T>], y: &[ModInt<T>]) -> Self {
            assert!(x.len() > 0 && x.len() == y.len());
            let size = x.len().next_power_of_two();
            let mut p = vec![Polynomial::one(); 2 * size];
            for (p, x) in p[size..].iter_mut().zip(x.iter()) {
                *p = Polynomial::new(vec![-*x, ModInt::one()]);
            }
            for i in (1..size).rev() {
                p[i] = p[2 * i].mul(&p[2 * i + 1]);
            }
            let z = p[1].derivative().multi_eval(x);
            let mut a = vec![Polynomial::zero(); 2 * size];
            for (a, (z, y)) in a[size..].iter_mut().zip(z.iter().zip(y.iter())) {
                *a = Polynomial::new(vec![*y * z.inv()]);
            }
            for i in (1..size).rev() {
                a[i] = a[2 * i]
                    .mul(&p[2 * i + 1])
                    .add(&a[2 * i + 1].mul(&p[2 * i]));
            }
            a.swap_remove(1)
        }
    }
}

// ---------- begin polynomial ----------
//https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 より
macro_rules! input {
    (source = $s:expr, $($r:tt)*) => {
        let mut iter = $s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
    ($($r:tt)*) => {
        let s = {
            use std::io::Read;
            let mut s = String::new();
            std::io::stdin().read_to_string(&mut s).unwrap();
            s
        };
        let mut iter = s.split_whitespace();
        input_inner!{iter, $($r)*}
    };
}

macro_rules! input_inner {
    ($iter:expr) => {};
    ($iter:expr, ) => {};
    ($iter:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($iter, $t);
        input_inner!{$iter $($r)*}
    };
}

macro_rules! read_value {
    ($iter:expr, ( $($t:tt),* )) => {
        ( $(read_value!($iter, $t)),* )
    };
    ($iter:expr, [ $t:tt ; $len:expr ]) => {
        (0..$len).map(|_| read_value!($iter, $t)).collect::<Vec<_>>()
    };
    ($iter:expr, chars) => {
        read_value!($iter, String).chars().collect::<Vec<char>>()
    };
    ($iter:expr, bytes) => {
        read_value!($iter, String).bytes().collect::<Vec<u8>>()
    };
    ($iter:expr, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

use modint::*;
use poly::*;

struct P;
impl ConstantModulo for P {
    const MOD: u32 = 998_244_353;
}

impl transform::NTTFriendly for P {
    fn order() -> usize {
        1 << 23
    }
    fn zeta() -> u32 {
        let p = Self::MOD as u64;
        mod_pow(3, (p - 1) >> 23, p) as u32
    }
}

type M = ModInt<P>;
type Poly = Polynomial<P>;

fn calc(a: &[(Poly, Poly)]) -> (Poly, Poly) {
    let n = a.len();
    if n == 1 {
        return a[0].clone();
    }
    let m = n / 2;
    let (l, r) = a.split_at(m);
    let p = calc(l);
    let q = calc(r);
    (p.0.mul(&q.1).add(&(p.1.mul(&q.0))), p.1.mul(&q.1))
}

fn run() {
    input! {
        n: usize,
        m: usize,
        a: [M; n],
    }
    let a = a.into_iter().map(|a| (Poly::one(), Polynomial::new(vec![M::one(), -a]))).collect::<Vec<_>>();
    let (nu, de) = calc(&a);
    let mut ans = nu.mul(&de.inverse(m + 1)).a;
    ans.resize(m + 1, M::zero());
    ans.truncate(m + 1);
    let mut s = String::new();
    for a in ans.iter().skip(1) {
        s.push_str(&format!("{} ", a));
    }
    s.pop();
    println!("{}", s);
}

fn main() {
    run();
}