#779088 (Rust) No.2013 Can we meet?

提出ソース
結果

問題	No.2013 Can we meet?
ユーザー	akakimidori
提出日時	2022-07-16 02:02:27
言語	Rust (1.77.0)
結果	AC
実行時間	343 ms / 2,500 ms
コード長	24,711 bytes
コンパイル時間	1,741 ms
コンパイル使用メモリ	165,876 KB
実行使用メモリ	20,244 KB
最終ジャッジ日時	2023-09-10 08:48:36
合計ジャッジ時間	7,950 ms
ジャッジサーバーID （参考情報）	judge12 / judge13
このコードへのチャレンジ（β）
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 4,376 KB
testcase_01	AC	1 ms 4,376 KB
testcase_02	AC	1 ms 4,376 KB
testcase_03	AC	1 ms 4,376 KB
testcase_04	AC	1 ms 4,376 KB
testcase_05	AC	1 ms 4,380 KB
testcase_06	AC	1 ms 4,376 KB
testcase_07	AC	1 ms 4,380 KB
testcase_08	AC	1 ms 4,376 KB
testcase_09	AC	1 ms 4,380 KB
testcase_10	AC	1 ms 4,380 KB
testcase_11	AC	1 ms 4,380 KB
testcase_12	AC	1 ms 4,376 KB
testcase_13	AC	1 ms 4,376 KB
testcase_14	AC	1 ms 4,376 KB
testcase_15	AC	4 ms 4,376 KB
testcase_16	AC	5 ms 4,376 KB
testcase_17	AC	6 ms 4,384 KB
testcase_18	AC	5 ms 4,376 KB
testcase_19	AC	5 ms 4,380 KB
testcase_20	AC	5 ms 4,380 KB
testcase_21	AC	1 ms 4,380 KB
testcase_22	AC	5 ms 4,380 KB
testcase_23	AC	6 ms 4,380 KB
testcase_24	AC	336 ms 20,244 KB
testcase_25	AC	328 ms 20,232 KB
testcase_26	AC	336 ms 20,244 KB
testcase_27	AC	329 ms 20,240 KB
testcase_28	AC	338 ms 20,188 KB
testcase_29	AC	335 ms 20,228 KB
testcase_30	AC	325 ms 20,144 KB
testcase_31	AC	337 ms 20,192 KB
testcase_32	AC	7 ms 4,380 KB
testcase_33	AC	7 ms 4,384 KB
testcase_34	AC	343 ms 20,228 KB
testcase_35	AC	327 ms 20,228 KB
testcase_36	AC	332 ms 20,192 KB
testcase_37	AC	7 ms 4,376 KB
testcase_38	AC	7 ms 4,384 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

raw source code
// F: 初めてたどり着く確率
// G: 戻ってくる確率
// H: 着く確率
// F * G = H

fn run() {
    input! {
        n: usize,
        s: (i64, i64),
        t: (i64, i64),
        a: usize,
        b: usize,
        w: [M; n],
    }
    let t = ((t.0 - s.0).abs(), (t.1 - s.1).abs());
    let sum = t.0 + t.1;
    if sum % 2 != 0 || sum as usize > 2 * n {
        println!("0");
        return;
    }
    let t = (t.0 as usize, t.1 as usize);
    let p = M::from(a) * M::from(a + b).inv();
    let pc = precalc::Precalc::new(4 * n);
    let mut x = vec![M::zero(); 2 * n + 1];
    for (i, x) in x.iter_mut().enumerate() {
        if i >= t.0 && (i - t.0) % 2 == 0 {
            let k = (i - t.0) / 2;
            *x = pc.comb(i, k) * M::new(2).inv().pow(i as u64) * p.pow(i as u64);
        }
        *x *= pc.ifact(i);
    }
    let mut y = vec![M::zero(); 2 * n + 1];
    for (i, y) in y.iter_mut().enumerate() {
        if i >= t.1 && (i - t.1) % 2 == 0 {
            let k = (i - t.1) / 2;
            *y = pc.comb(i, k) * M::new(2).inv().pow(i as u64) * (M::one() - p).pow(i as u64);
        }
        *y *= pc.ifact(i);
    }
    let mut z = x.multiply(&y);
    z.truncate(2 * n + 1);
    for (i, z) in z.iter_mut().enumerate() {
        *z *= pc.fact(i);
    }
    let mut row = vec![M::zero(); 2 * n + 1];
    let mut col = vec![M::zero(); 2 * n + 1];
    for i in (0..=(2 * n)).step_by(2) {
        if i % 2 == 0 {
            row[i] = pc.comb(i, i / 2) * M::new(2).inv().pow(i as u64) * p.pow(i as u64);
            col[i] = pc.comb(i, i / 2) * M::new(2).inv().pow(i as u64) * (M::one() - p).pow(i as u64);
            row[i] *= pc.ifact(i);
            col[i] *= pc.ifact(i);
        }
    }
    let mut zero = row.multiply(&col);
    for i in 0..=(2 * n) {
        zero[i] *= pc.fact(i);
    }
    zero.truncate(2 * n + 1);
    let res = z.multiply(&zero.inverse(2 * n + 1));
    let mut ans = M::zero();
    for i in (2..=(2 * n)).step_by(2) {
        let p = res[i];
        ans += w[i / 2 - 1] * p;
    }
    println!("{}", ans);
}

fn main() {
    run();
}

// ---------- begin input macro ----------
// reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[macro_export]
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_export]
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_export]
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")
    };
}
// ---------- end input macro ----------
// ---------- begin ModInt ----------
// モンゴメリ乗算を用いる
// ほぼCodeforces用
// 注意
// new_unchecked は値xが 0 <= x < modulo であることを仮定
// ModInt の中身は正規化された値で持ってるので直接読んだり書いたりするとぶっ壊れる
// 奇素数のみ
mod modint {

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

    pub trait Modulo {
        fn modulo() -> u32;
        fn rem() -> u32;
        fn ini() -> u64;
        fn reduce(x: u64) -> u32 {
            debug_assert!(x < (Self::modulo() as u64) << 32);
            let b = (x as u32 * Self::rem()) as u64;
            let t = x + b * Self::modulo() as u64;
            let mut c = (t >> 32) as u32;
            if c >= Self::modulo() {
                c -= Self::modulo();
            }
            c as u32
        }
    }

    #[allow(dead_code)]
    pub enum Mod1_000_000_007 {}

    impl Modulo for Mod1_000_000_007 {
        fn modulo() -> u32 {
            1_000_000_007
        }
        fn rem() -> u32 {
            2226617417
        }
        fn ini() -> u64 {
            582344008
        }
    }

    #[allow(dead_code)]
    pub enum Mod998_244_353 {}

    impl Modulo for Mod998_244_353 {
        fn modulo() -> u32 {
            998_244_353
        }
        fn rem() -> u32 {
            998244351
        }
        fn ini() -> u64 {
            932051910
        }
    }

    #[allow(dead_code)]
    pub fn generate_umekomi_modulo(p: u32) {
        assert!(
            p < (1 << 31)
                && p > 2
                && p & 1 == 1
                && (2u32..).take_while(|v| v * v <= p).all(|k| p % k != 0)
        );
        let mut t = 1u32;
        let mut s = !p + 1;
        let mut n = !0u32 >> 2;
        while n > 0 {
            if n & 1 == 1 {
                t *= s;
            }
            s *= s;
            n >>= 1;
        }
        let mut ini = (1u64 << 32) % p as u64;
        ini = (ini << 32) % p as u64;
        assert!(t * p == !0);
        println!("pub enum Mod{} {{}}", p);
        println!("impl Modulo for Mod{} {{", p);
        println!("    fn modulo() -> u32 {{");
        println!("        {}", p);
        println!("    }}");
        println!("    fn rem() -> u32 {{");
        println!("        {}", t);
        println!("    }}");
        println!("    fn ini() -> u64 {{");
        println!("        {}", ini);
        println!("    }}");
        println!("}}");
        let mut f = vec![];
        let mut n = p - 1;
        for i in 2.. {
            if i * i > n {
                break;
            }
            if n % i == 0 {
                f.push(i);
                while n % i == 0 {
                    n /= i;
                }
            }
        }
        if n > 1 {
            f.push(n);
        }
        let mut order = 1;
        let mut n = p - 1;
        while n % 2 == 0 {
            n /= 2;
            order <<= 1;
        }
        let z = (2u64..)
            .find(|z| {
                f.iter()
                    .all(|f| mod_pow(*z, ((p - 1) / *f) as u64, p as u64) != 1)
            })
            .unwrap();
        let zeta = mod_pow(z, ((p - 1) / order) as u64, p as u64);
        println!("impl transform::NTTFriendly for Mod{} {{", p);
        println!("    fn order() -> usize {{");
        println!("        {}", order);
        println!("    }}");
        println!("    fn zeta() -> u32 {{");
        println!("        {}", zeta);
        println!("    }}");
        println!("}}");
    }

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

    impl<T> Clone for ModInt<T> {
        fn clone(&self) -> Self {
            ModInt::build(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();
            }
            Self::build(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 = self.0 - rhs.0;
            if self.0 < rhs.0 {
                d += T::modulo();
            }
            Self::build(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 {
            Self::build(T::reduce(self.0 as u64 * rhs.0 as u64))
        }
    }

    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::build(T::modulo() - self.0)
            }
        }
    }

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

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

    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<u64> for ModInt<T> {
        fn from(val: u64) -> ModInt<T> {
            ModInt::new_unchecked((val % T::modulo() as u64) 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> {
        fn build(d: u32) -> Self {
            ModInt(d, PhantomData)
        }
        pub fn zero() -> Self {
            Self::build(0)
        }
        pub fn is_zero(&self) -> bool {
            self.0 == 0
        }
    }

    #[allow(dead_code)]
    impl<T: Modulo> ModInt<T> {
        pub fn new_unchecked(d: u32) -> Self {
            Self::build(T::reduce(d as u64 * T::ini()))
        }
        pub fn new(d: u32) -> Self {
            Self::new_unchecked(d % T::modulo())
        }
        pub fn one() -> Self {
            Self::new_unchecked(1)
        }
        pub fn get(&self) -> u32 {
            T::reduce(self.0 as u64)
        }
        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.is_zero());
            self.pow((T::modulo() - 2) as u64)
        }
    }

    pub fn mod_pow(mut r: u64, mut n: u64, m: u64) -> u64 {
        let mut t = 1 % m;
        while n > 0 {
            if n & 1 == 1 {
                t = t * r % m;
            }
            r = r * r % 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 ----------

use modint::*;

pub trait NTTFriendly: modint::Modulo {
    fn order() -> usize;
    fn zeta() -> u32;
}

type M = ModInt<Mod998_244_353>;

impl NTTFriendly for Mod998_244_353 {
    fn order() -> usize {
        8388608
    }
    fn zeta() -> u32 {
        15311432
    }
}

// 列に対する命令をテキトーに詰めあわせ
// modint, primitive type の２つあたりで使うことを想定
// +, -, *
// zero を要求してないのに仮定してる場所がある
//
// 何も考えずに書き始めたらいろいろよくわからないことになった
// 整理
// 長さが等しいときの加算、減算、dot積はok
// 長さが異なるときはどうする？
// 0埋めされてるというイメージなので
// 加算、減算は素直だがdot積はイマイチ
// dot積だけ長さが等しいとしておく?
// あるいは0埋めのイメージを消すか

use std::ops::*;

pub trait Zero: Sized + Add<Output = Self> {
    fn zero() -> Self;
}

pub fn zero<T: Zero>() -> T {
    T::zero()
}

impl<T: Modulo> Zero for ModInt<T> {
    fn zero() -> Self {
        Self::zero()
    }
}

impl Zero for usize {
    fn zero() -> Self {
        0
    }
}

pub trait ArrayAdd {
    type Item;
    fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArrayAdd for [T]
where
    T: Zero + Copy,
{
    type Item = T;
    fn add(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        let mut c = vec![T::zero(); self.len().max(rhs.len())];
        c[..self.len()].copy_from_slice(self);
        c.add_assign(rhs);
        c
    }
}

pub trait ArrayAddAssign {
    type Item;
    fn add_assign(&mut self, rhs: &[Self::Item]);
}

impl<T> ArrayAddAssign for [T]
where
    T: Add<Output = T> + Copy,
{
    type Item = T;
    fn add_assign(&mut self, rhs: &[Self::Item]) {
        assert!(self.len() >= rhs.len());
        self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x + *a);
    }
}

impl<T> ArrayAddAssign for Vec<T>
where
    T: Zero + Add<Output = T> + Copy,
{
    type Item = T;
    fn add_assign(&mut self, rhs: &[Self::Item]) {
        if self.len() < rhs.len() {
            self.resize(rhs.len(), T::zero());
        }
        self.as_mut_slice().add_assign(rhs);
    }
}

pub trait ArraySub {
    type Item;
    fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArraySub for [T]
where
    T: Zero + Sub<Output = T> + Copy,
{
    type Item = T;
    fn sub(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        let mut c = vec![T::zero(); self.len().max(rhs.len())];
        c[..self.len()].copy_from_slice(self);
        c.sub_assign(rhs);
        c
    }
}

pub trait ArraySubAssign {
    type Item;
    fn sub_assign(&mut self, rhs: &[Self::Item]);
}

impl<T> ArraySubAssign for [T]
where
    T: Sub<Output = T> + Copy,
{
    type Item = T;
    fn sub_assign(&mut self, rhs: &[Self::Item]) {
        assert!(self.len() >= rhs.len());
        self.iter_mut().zip(rhs).for_each(|(x, a)| *x = *x - *a);
    }
}

impl<T> ArraySubAssign for Vec<T>
where
    T: Zero + Sub<Output = T> + Copy,
{
    type Item = T;
    fn sub_assign(&mut self, rhs: &[Self::Item]) {
        if self.len() < rhs.len() {
            self.resize(rhs.len(), T::zero());
        }
        self.as_mut_slice().sub_assign(rhs);
    }
}

pub trait ArrayDot {
    type Item;
    fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArrayDot for [T]
where
    T: Mul<Output = T> + Copy,
{
    type Item = T;
    fn dot(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        assert!(self.len() == rhs.len());
        self.iter().zip(rhs).map(|p| *p.0 * *p.1).collect()
    }
}

pub trait ArrayDotAssign {
    type Item;
    fn dot_assign(&mut self, rhs: &[Self::Item]);
}

impl<T> ArrayDotAssign for [T]
where
    T: MulAssign + Copy,
{
    type Item = T;
    fn dot_assign(&mut self, rhs: &[Self::Item]) {
        assert!(self.len() == rhs.len());
        self.iter_mut().zip(rhs).for_each(|(x, a)| *x *= *a);
    }
}

pub trait ArrayMul {
    type Item;
    fn mul(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArrayMul for [T]
where
    T: Zero + Mul<Output = T> + Copy,
{
    type Item = T;
    fn mul(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        if self.is_empty() || rhs.is_empty() {
            return vec![];
        }
        let mut res = vec![zero(); self.len() + rhs.len() - 1];
        for (i, a) in self.iter().enumerate() {
            for (c, b) in res[i..].iter_mut().zip(rhs) {
                *c = *c + *a * *b;
            }
        }
        res
    }
}

pub trait ArrayNTT {
    type Item;
    fn ntt(&mut self);
    fn intt(&mut self);
    fn multiply(&self, rhs: &[Self::Item]) -> Vec<Self::Item>;
}

impl<T> ArrayNTT for [ModInt<T>]
where
    T: NTTFriendly,
{
    type Item = ModInt<T>;
    fn ntt(&mut self) {
        let f = self;
        let n = f.len();
        assert!(n.count_ones() == 1);
        assert!(n <= T::order());
        let len = n.trailing_zeros() as usize;
        let mut es = [ModInt::zero(); 30];
        let mut ies = [ModInt::zero(); 30];
        let mut sum_e = [ModInt::zero(); 30];
        let cnt2 = T::order().trailing_zeros() as usize;
        let mut e = ModInt::new_unchecked(T::zeta());
        let mut ie = e.inv();
        for i in (2..=cnt2).rev() {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e = e * e;
            ie = ie * ie;
        }
        let mut now = ModInt::one();
        for i in 0..(cnt2 - 1) {
            sum_e[i] = es[i] * now;
            now *= ies[i];
        }
        for ph in 1..=len {
            let p = 1 << (len - ph);
            let mut now = ModInt::one();
            for (i, f) in f.chunks_exact_mut(2 * p).enumerate() {
                let (x, y) = f.split_at_mut(p);
                for (x, y) in x.iter_mut().zip(y.iter_mut()) {
                    let l = *x;
                    let r = *y * now;
                    *x = l + r;
                    *y = l - r;
                }
                now *= sum_e[(!i).trailing_zeros() as usize];
            }
        }
    }
    fn intt(&mut self) {
        let f = self;
        let n = f.len();
        assert!(n.count_ones() == 1);
        assert!(n <= T::order());
        let len = n.trailing_zeros() as usize;
        let mut es = [ModInt::zero(); 30];
        let mut ies = [ModInt::zero(); 30];
        let mut sum_ie = [ModInt::zero(); 30];
        let cnt2 = T::order().trailing_zeros() as usize;
        let mut e = ModInt::new_unchecked(T::zeta());
        let mut ie = e.inv();
        for i in (2..=cnt2).rev() {
            es[i - 2] = e;
            ies[i - 2] = ie;
            e = e * e;
            ie = ie * ie;
        }
        let mut now = ModInt::one();
        for i in 0..(cnt2 - 1) {
            sum_ie[i] = ies[i] * now;
            now *= es[i];
        }
        for ph in (1..=len).rev() {
            let p = 1 << (len - ph);
            let mut inow = ModInt::one();
            for (i, f) in f.chunks_exact_mut(2 * p).enumerate() {
                let (x, y) = f.split_at_mut(p);
                for (x, y) in x.iter_mut().zip(y.iter_mut()) {
                    let l = *x;
                    let r = *y;
                    *x = l + r;
                    *y = (l - r) * inow;
                }
                inow *= sum_ie[(!i).trailing_zeros() as usize];
            }
        }
        let ik = ModInt::new_unchecked((T::modulo() + 1) >> 1).pow(len as u64);
        for f in f.iter_mut() {
            *f *= ik;
        }
    }
    fn multiply(&self, rhs: &[Self::Item]) -> Vec<Self::Item> {
        if self.len().min(rhs.len()) <= 32 {
            return self.mul(rhs);
        }
        let size = (self.len() + rhs.len() - 1).next_power_of_two();
        let mut f = vec![ModInt::zero(); size];
        let mut g = vec![ModInt::zero(); size];
        f[..self.len()].copy_from_slice(self);
        g[..rhs.len()].copy_from_slice(rhs);
        f.ntt();
        g.ntt();
        f.dot_assign(&g);
        f.intt();
        f.truncate(self.len() + rhs.len() - 1);
        f
    }
}

pub trait PolynomialOperation {
    type Item;
    fn eval(&self, x: Self::Item) -> Self::Item;
    fn derivative(&self) -> Vec<Self::Item>;
    fn integral(&self) -> Vec<Self::Item>;
}

impl<T: Modulo> PolynomialOperation for [ModInt<T>] {
    type Item = ModInt<T>;
    fn eval(&self, x: Self::Item) -> Self::Item {
        self.iter().rev().fold(ModInt::zero(), |s, a| s * x + *a)
    }
    fn derivative(&self) -> Vec<Self::Item> {
        if self.len() <= 1 {
            return vec![];
        }
        self[1..]
            .iter()
            .enumerate()
            .map(|(k, a)| ModInt::new_unchecked(k as u32 + 1) * *a)
            .collect()
    }
    fn integral(&self) -> Vec<Self::Item> {
        if self.is_empty() {
            return vec![];
        }
        let mut inv = vec![ModInt::one(); self.len() + 1];
        let mut mul = ModInt::zero();
        for i in 1..=self.len() {
            mul += ModInt::one();
            inv[i] = inv[i - 1] * mul;
        }
        let mut prod = inv[self.len()].inv();
        for i in (1..=self.len()).rev() {
            inv[i] = self[i - 1] * inv[i - 1] * prod;
            prod *= mul;
            mul -= ModInt::one();
        }
        inv[0] = ModInt::zero();
        inv
    }
}

pub trait FPSOperation {
    type Item;
    fn inverse(&self, n: usize) -> Vec<Self::Item>;
    fn log(&self, n: usize) -> Vec<Self::Item>;
    fn exp(&self, n: usize) -> Vec<Self::Item>;
}

impl<T: NTTFriendly> FPSOperation for [ModInt<T>] {
    type Item = ModInt<T>;
    fn inverse(&self, n: usize) -> Vec<Self::Item> {
        assert!(self.len() > 0 && !self[0].is_zero());
        let len = n.next_power_of_two();
        assert!(2 * len <= T::order());
        let mut b = vec![ModInt::zero(); n];
        b[0] = self[0].inv();
        let mut f = Vec::with_capacity(2 * len);
        let mut g = Vec::with_capacity(2 * len);
        let mut size = 1;
        while size < n {
            g.clear();
            g.extend(b.iter().take(size));
            g.resize(2 * size, ModInt::zero());
            f.clear();
            f.extend(self.iter().take(2 * size));
            f.resize(2 * size, ModInt::zero());
            f.ntt();
            g.ntt();
            f.dot_assign(&g);
            f.intt();
            f[..size].iter_mut().for_each(|f| *f = ModInt::zero());
            f.ntt();
            f.dot_assign(&g);
            f.intt();
            for (b, g) in b[size..].iter_mut().zip(&f[size..]) {
                *b = *b - *g;
            }
            size *= 2;
        }
        b
    }
    fn log(&self, n: usize) -> Vec<Self::Item> {
        assert!(self.get(0).map_or(false, |p| p.get() == 1));
        let mut b = self.derivative().multiply(&self.inverse(n));
        b.truncate(n - 1);
        let mut b = b.integral();
        b.resize(n, ModInt::zero());
        b
    }
    fn exp(&self, n: usize) -> Vec<Self::Item> {
        assert!(self.get(0).map_or(true, |a| a.is_zero()));
        assert!(n <= T::order());
        let mut b = vec![ModInt::one()];
        let mut size = 1;
        while size < n {
            size <<= 1;
            let f = b.log(size);
            let g = self[..self.len().min(size)].sub(&f);
            b = b.multiply(&g).add(&b);
            b.truncate(size);
        }
        b.truncate(n);
        b.resize(n, ModInt::zero());
        b
    }
}

// test
//  yuki907: https://yukicoder.me/submissions/712523
//  hhkb2020: https://atcoder.jp/contests/hhkb2020/submissions/26997806