結果

問題 No.1068 #いろいろな色 / Red and Blue and more various colors (Hard)
ユーザー akakimidoriakakimidori
提出日時 2020-05-29 22:09:23
言語 Rust
(1.77.0)
結果
AC  
実行時間 547 ms / 3,500 ms
コード長 17,389 bytes
コンパイル時間 1,409 ms
コンパイル使用メモリ 176,000 KB
実行使用メモリ 20,808 KB
最終ジャッジ日時 2024-04-23 22:46:03
合計ジャッジ時間 12,059 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 1 ms
6,812 KB
testcase_01 AC 1 ms
6,940 KB
testcase_02 AC 1 ms
6,944 KB
testcase_03 AC 10 ms
6,944 KB
testcase_04 AC 7 ms
6,940 KB
testcase_05 AC 7 ms
6,940 KB
testcase_06 AC 6 ms
6,940 KB
testcase_07 AC 6 ms
6,940 KB
testcase_08 AC 7 ms
6,940 KB
testcase_09 AC 8 ms
6,940 KB
testcase_10 AC 4 ms
6,940 KB
testcase_11 AC 5 ms
6,944 KB
testcase_12 AC 3 ms
6,940 KB
testcase_13 AC 510 ms
20,592 KB
testcase_14 AC 508 ms
20,588 KB
testcase_15 AC 547 ms
20,588 KB
testcase_16 AC 547 ms
20,596 KB
testcase_17 AC 520 ms
20,464 KB
testcase_18 AC 525 ms
20,592 KB
testcase_19 AC 521 ms
20,464 KB
testcase_20 AC 502 ms
20,592 KB
testcase_21 AC 505 ms
20,464 KB
testcase_22 AC 511 ms
20,588 KB
testcase_23 AC 530 ms
20,588 KB
testcase_24 AC 531 ms
20,464 KB
testcase_25 AC 529 ms
20,572 KB
testcase_26 AC 516 ms
20,592 KB
testcase_27 AC 514 ms
20,588 KB
testcase_28 AC 505 ms
20,808 KB
testcase_29 AC 499 ms
18,980 KB
testcase_30 AC 516 ms
18,852 KB
testcase_31 AC 0 ms
6,940 KB
権限があれば一括ダウンロードができます

ソースコード

diff # 

// ---------- begin ModInt ----------
mod modint {
pub const MOD: u32 = 998_244_353;

#[derive(Clone, Copy)]
pub struct ModInt(pub u32);
impl std::ops::Add for ModInt {
    type Output = ModInt;
    fn add(self, rhs: ModInt) -> ModInt {
        let mut d = self.0 + rhs.0;
        if d >= MOD {
            d -= MOD;
        }
        ModInt(d)
    }
}
impl std::ops::Sub for ModInt {
    type Output = ModInt;
    fn sub(self, rhs: ModInt) -> ModInt {
        let d = if self.0 >= rhs.0 {
            self.0 - rhs.0
        } else {
            self.0 + MOD - rhs.0
        };
        ModInt(d)
    }
}
impl std::ops::Mul for ModInt {
    type Output = ModInt;
    fn mul(self, rhs: ModInt) -> ModInt {
        ModInt((self.0 as u64 * rhs.0 as u64 % MOD as u64) as u32)
    }
}
impl std::ops::Neg for ModInt {
    type Output = ModInt;
    fn neg(self) -> ModInt {
        if self.0 == 0 {
            self
        } else {
            ModInt(MOD - self.0)
        }
    }
}
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: ModInt) {
        *self = *self + rhs;
    }
}
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: ModInt) {
        *self = *self - rhs;
    }
}
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: ModInt) {
        *self = *self * rhs;
    }
}
impl std::fmt::Display for ModInt {
    fn fmt<'a>(&self, f: &mut std::fmt::Formatter<'a>) -> std::fmt::Result {
        write!(f, "{}", self.0)
    }
}
impl std::str::FromStr for ModInt {
    type Err = std::num::ParseIntError;
    fn from_str(s: &str) -> Result<Self, Self::Err> {
        let val = s.parse::<u32>()?;
        Ok(ModInt::new(val))
    }
}
impl From<usize> for ModInt {
    fn from(v: usize) -> Self {
        ModInt((v % MOD as usize) as u32)
    }
}
#[allow(dead_code)]
impl ModInt {
    pub fn new(v: u32) -> ModInt {
        ModInt(v % MOD)
    }
    pub fn zero() -> ModInt {
        ModInt(0)
    }
    pub fn one() -> ModInt {
        ModInt(1)
    }
    pub fn zeta() -> ModInt {
        ModInt(3)
    }
    pub fn pow(self, mut n: u32) -> ModInt {
        let mut t = ModInt::one();
        let mut s = self;
        while n > 0 {
            if n & 1 == 1 {
                t = t * s;
            }
            s = s * s;
            n >>= 1;
        }
        t
    }
    pub fn inv(self) -> ModInt {
        assert!(self.0 > 0, "ModInt inv called with 0");
        self.pow(MOD - 2)
    }
}
}
// ---------- end ModInt ----------
// ---------- begin Precalc ----------
#[allow(dead_code)]
mod precalc {
    use super::modint::*;
    struct Precalc {
        inv: Vec<ModInt>,
        fact: Vec<ModInt>,
        ifact: Vec<ModInt>,
    }
    impl Precalc {
        pub fn new(n: usize) -> Precalc {
            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) {
                inv[i] = -inv[MOD as usize % i] * ModInt(MOD / i as u32);
                fact[i] = fact[i - 1] * i.into();
                ifact[i] = ifact[i - 1] * inv[i];
            }
            Precalc {
                inv: inv,
                fact: fact,
                ifact: ifact,
            }
        }
        pub fn fact(&self, n: usize) -> ModInt {
            self.fact[n]
        }
        pub fn comb(&self, n: usize, k: usize) -> ModInt {
            if n < k {
                ModInt::zero()
            } else {
                self.fact[n] * self.ifact[k] * self.ifact[n - k]
            }
        }
        pub fn inv(&self, n: usize) -> ModInt {
            self.inv[n]
        }
    }
}
// ---------- end Precalc ----------
// ---------- begin NTT ----------
#[allow(dead_code)]
mod transform {
    use super::modint::*;
    pub fn ntt(f: &mut [ModInt]) {
        let n = f.len();
        assert!(n.count_ones() == 1);
        let len = n.trailing_zeros() as usize;
        let mut zeta = Vec::with_capacity(len);
        let mut r = ModInt(3).pow((MOD - 1) >> len);
        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(f: &mut [ModInt]) {
        let n = f.len();
        assert!(n.count_ones() == 1);
        let len = n.trailing_zeros() as usize;
        let mut zeta = Vec::with_capacity(len);
        let mut r = ModInt(3).inv().pow((MOD - 1) >> len);
        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(f.len() as u32).inv();
        for f in f.iter_mut() {
            *f *= ik;
        }
    }
    pub fn multiply(a: &[ModInt], b: &[ModInt]) -> Vec<ModInt> {
        if a.is_empty() || b.is_empty() {
            return vec![];
        }
        let n = a.len() + b.len() - 1;
        let mut k = 1;
        while k < n {
            k *= 2;
        }
        assert!(k <= (1 << 23));
        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;
    use std;
    #[derive(Clone)]
    pub struct Polynomial {
        pub a: Vec<ModInt>,
    }
    impl Polynomial {
        pub fn new(a: Vec<ModInt>) -> Self {
            let mut a = Polynomial { a: a };
            a.fix();
            a
        }
        pub fn from_slice(a: &[ModInt]) -> 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 {
            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) -> ModInt {
            let mut ans = ModInt::zero();
            for a in self.a.iter().rev() {
                ans = ans * x + *a;
            }
            ans
        }
        pub fn fix(&mut self) {
            while let Some(&v) = self.a.last() {
                if v.0 == 0 {
                    self.a.pop();
                } else {
                    break;
                }
            }
        }
        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(i as u32 + 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[MOD as usize % k] * ModInt(MOD / k as u32);
                *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;
            }
        }
        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[0].0 > 0);
            let len = n.next_power_of_two();
            assert!(2 * len <= (1 << 23));
            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.len() > 0 && self.a[0].0 == 0 && n <= (1 << 23));
            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]) -> Vec<ModInt> {
            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], y: &[ModInt]) -> 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)
        }
    }
}
// ---------- end 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, usize1) => {
        read_value!($iter, usize) - 1
    };
    ($iter:expr, $t:ty) => {
        $iter.next().unwrap().parse::<$t>().expect("Parse error")
    };
}

//

use poly::*;
use modint::*;
use std::io::Write;

fn calc(a: &[Polynomial]) -> Polynomial {
    if a.len() == 1 {
        a[0].clone()
    } else {
        let m = a.len() / 2;
        let (a, b) = a.split_at(m);
        calc(a).mul(&calc(b))
    }
}

fn run() {
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    input! {
        n: usize,
        q: usize,
        a: [usize; n],
        b: [usize; q],
    }
    let a = a.into_iter().map(|a| {
        let a = ModInt::from(a - 1);
        Polynomial::from_slice(&[a, ModInt::one()])
    }).collect::<Vec<_>>();
    let ans = calc(&a);
    for b in b {
        writeln!(out, "{}", ans.get(b)).ok();
    }
}

fn main() {
    run();
}
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