結果

問題 No.1529 Constant Lcm
ユーザー ngtkanangtkana
提出日時 2021-06-05 17:24:22
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 18 ms / 3,000 ms
コード長 33,609 bytes
コンパイル時間 12,620 ms
コンパイル使用メモリ 400,892 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-05-01 11:22:49
合計ジャッジ時間 13,934 ms
ジャッジサーバーID
(参考情報)
judge3 / judge1
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
6,816 KB
testcase_01 AC 1 ms
6,816 KB
testcase_02 AC 1 ms
6,816 KB
testcase_03 AC 0 ms
6,944 KB
testcase_04 AC 1 ms
6,944 KB
testcase_05 AC 1 ms
6,944 KB
testcase_06 AC 1 ms
6,940 KB
testcase_07 AC 1 ms
6,940 KB
testcase_08 AC 1 ms
6,944 KB
testcase_09 AC 1 ms
6,940 KB
testcase_10 AC 18 ms
6,944 KB
testcase_11 AC 5 ms
6,940 KB
testcase_12 AC 1 ms
6,944 KB
testcase_13 AC 9 ms
6,944 KB
testcase_14 AC 8 ms
6,944 KB
testcase_15 AC 8 ms
6,944 KB
testcase_16 AC 9 ms
6,944 KB
testcase_17 AC 5 ms
6,944 KB
testcase_18 AC 5 ms
6,940 KB
testcase_19 AC 9 ms
6,944 KB
testcase_20 AC 17 ms
6,944 KB
testcase_21 AC 18 ms
6,944 KB
testcase_22 AC 18 ms
6,940 KB
testcase_23 AC 18 ms
6,944 KB
testcase_24 AC 18 ms
6,940 KB
testcase_25 AC 18 ms
6,940 KB
権限があれば一括ダウンロードができます
コンパイルメッセージ
warning: unused imports: `PrimeNumbers`, `lpd_sieve::LpdSieve`
   --> src/main.rs:749:9
    |
749 |         lpd_sieve::LpdSieve,
    |         ^^^^^^^^^^^^^^^^^^^
750 |         sieve::Sieve,
751 |         sieve_base::{PrimeFactorsByLookup, PrimeFactorsByTrialDivision, PrimeNumbers},
    |                                                                         ^^^^^^^^^^^^
    |
    = note: `#[warn(unused_imports)]` on by default

warning: unused imports: `Leaf`, `Tuple`, `VecLen`
   --> src/main.rs:773:27
    |
773 |             multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen},
    |                           ^^^^                                 ^^^^^  ^^^^^^

warning: unused import: `with_str`
    --> src/main.rs:1029:35
     |
1029 |     pub use self::i::{with_stdin, with_str};
     |                                   ^^^^^^^^

warning: unused imports: `ParserTuple`, `Parser`, `RawTuple`, `Token`, `Usize1`
    --> src/main.rs:1032:28
     |
1032 |         pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
     |                            ^^^^^^  ^^^^^^^^^^^  ^^^^^^^^  ^^^^^  ^^^^^^

ソースコード

diff #

#[allow(unused_imports)]
#[cfg(feature = "dbg")]
use dbg::lg;
use erato::Sieve;
type Fp = fp::F998244353;

fn main() {
    let mut buf = ngtio::with_stdin();
    let n = buf.u32();
    let ans = Sieve::new()
        .prime_numbers::<u32>()
        .take_while(|&p| p <= n)
        .map(|p| {
            let mut n = n;
            let mut e = 0;
            let mut m = 0;
            while n % p == 0 {
                e += 1;
                m += 1;
                n /= p;
            }
            while p <= n {
                m += 1;
                n /= p;
            }
            let pow = if e == m && n == 1 { 2 * (m - 1) } else { m + e };
            Fp::new(p).pow(pow as u32)
        })
        .product::<Fp>();
    println!("{}", ans);
}

// fp {{{
#[allow(dead_code)]
mod fp {
    use std::{
        cmp::PartialEq,
        fmt,
        hash::{Hash, Hasher},
        iter::{successors, Product, Sum},
        marker::PhantomData,
        mem::swap,
        ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Neg, Sub, SubAssign},
    };
    pub trait Mod: Clone + Copy + Hash {
        const P: u32;
        const K: u32;
        const R2: u32 = ((1_u128 << 64) % Self::P as u128) as _; // 2 ^ 64 mod P
    }
    fn reduce<M: Mod>(x: u64) -> u32 {
        ((x + u64::from(M::K.wrapping_mul(x as u32)) * u64::from(M::P)) >> 32) as u32
    }
    pub fn fact_iter<M: Mod>() -> impl Iterator<Item = Fp<M>> {
        (1..).scan(Fp::new(1), |state, x| {
            let ans = *state;
            *state *= x;
            Some(ans)
        })
    }
    #[allow(clippy::missing_panics_doc)]
    pub fn fact_build<M: Mod>(n: usize) -> [Vec<Fp<M>>; 2] {
        if n == 0 {
            [Vec::new(), Vec::new()]
        } else {
            let fact = fact_iter::<M>().take(n).collect::<Vec<_>>();
            let mut fact_inv = vec![fact.last().unwrap().recip(); n];
            (1..n).rev().for_each(|i| fact_inv[i - 1] = fact_inv[i] * i);
            [fact, fact_inv]
        }
    }
    pub fn binom_iter<M: Mod>() -> impl Iterator<Item = Vec<Fp<M>>> {
        successors(Some(vec![Fp::new(1)]), |last| {
            let mut crr = last.clone();
            crr.push(Fp::new(0));
            crr[1..].iter_mut().zip(last).for_each(|(x, &y)| *x += y);
            Some(crr)
        })
    }
    #[macro_export]
    macro_rules! define_mod {
        ($(($Fp: ident, $Mod: ident, $mod: expr, $k: expr),)*) => {$(
            #[derive(Clone, Debug, Default, Hash, Copy)]
            pub struct $Mod {}
            impl Mod for $Mod {
                const P: u32 = $mod;
                const K: u32 = $k;
            }
            pub type $Fp = Fp<$Mod>;
        )*}
    }
    define_mod! {
        (F998244353, Mod998244353, 998_244_353, 998_244_351),
        (F1000000007, Mod1000000007, 1_000_000_007, 2_226_617_417),
        (F1012924417, Mod1012924417, 1_012_924_417, 1_012_924_415),
        (F924844033, Mod924844033, 924_844_033, 924_844_031),
    }
    #[derive(Clone, Default, Copy)]
    pub struct Fp<M> {
        value: u32,
        __marker: PhantomData<M>,
    }
    impl<M: Mod> Fp<M> {
        pub const P: u32 = M::P;
        pub fn new(value: u32) -> Self {
            Self::from_raw(reduce::<M>(u64::from(value) * u64::from(M::R2)))
        }
        pub fn value(self) -> u32 {
            let x = reduce::<M>(u64::from(self.value));
            if M::P <= x {
                x - M::P
            } else {
                x
            }
        }
        #[allow(clippy::many_single_char_names)]
        pub fn recip(self) -> Self {
            assert_ne!(self, Self::new(0), "0 はだめ。");
            let mut x = M::P as i32;
            let mut y = self.value() as i32;
            let mut u = 0;
            let mut v = 1;
            while y != 0 {
                let q = x / y;
                x -= q * y;
                u -= q * v;
                swap(&mut x, &mut y);
                swap(&mut u, &mut v);
            }
            debug_assert_eq!(x, 1);
            if u < 0 {
                debug_assert_eq!(v, M::P as i32);
                u += v;
            }
            Self::new(u as u32)
        }
        pub fn pow<T: Into<u64>>(self, exp: T) -> Self {
            let mut exp = exp.into();
            if exp == 0 {
                return Self::new(1);
            }
            let mut base = self;
            let mut acc = Self::new(1);
            while 1 < exp {
                if exp & 1 == 1 {
                    acc *= base;
                }
                exp /= 2;
                base *= base;
            }
            acc * base
        }
        fn from_raw(value: u32) -> Self {
            Self {
                value,
                __marker: PhantomData,
            }
        }
    }
    fn simplify(value: i32, p: i32) -> (i32, i32, i32) {
        if value.abs() < 10_000 {
            (value, 1, 0)
        } else {
            let mut q = p.div_euclid(value);
            let mut r = p.rem_euclid(value);
            if value <= 2 * r {
                q += 1;
                r -= value;
            }
            let (num, pden, ppden) = simplify(r, value);
            let den = ppden - q * pden;
            (num, den, pden)
        }
    }
    macro_rules! impl_from_large_int {
        ($($T: ty), *$(,)?) => {$(
            impl<M: Mod> From<$T> for Fp<M> {
                fn from(x: $T) -> Self {
                    Self::new(x.rem_euclid(M::P as _) as u32)
                }
            }
        )*}
    }
    impl_from_large_int! {
        u32, u64, u128, usize,
        i32, i64, i128, isize,
    }
    macro_rules! impl_from_small_int {
        ($($T: ty), *$(,)?) => {$(
            impl<M: Mod> From<$T> for Fp<M> {
                fn from(x: $T) -> Self {
                    Self::new(x as u32)
                }
            }
        )*}
    }
    impl_from_small_int! {
        u8, u16,
        i8, i16,
    }
    impl<M: Mod> PartialEq for Fp<M> {
        fn eq(&self, other: &Self) -> bool {
            fn value<M: Mod>(fp: Fp<M>) -> u32 {
                if fp.value >= M::P {
                    fp.value - M::P
                } else {
                    fp.value
                }
            }
            value(*self) == value(*other)
        }
    }
    impl<M: Mod> Eq for Fp<M> {}
    impl<M: Mod> Hash for Fp<M> {
        fn hash<H: Hasher>(&self, state: &mut H) {
            self.value().hash(state);
        }
    }
    impl<M: Mod, T: Into<Self>> AddAssign<T> for Fp<M> {
        fn add_assign(&mut self, rhs: T) {
            self.value += rhs.into().value;
            if M::P * 2 <= self.value {
                self.value -= M::P * 2;
            }
        }
    }
    impl<M: Mod, T: Into<Self>> SubAssign<T> for Fp<M> {
        fn sub_assign(&mut self, rhs: T) {
            let rhs = rhs.into();
            if self.value < rhs.value {
                self.value += M::P * 2;
            }
            self.value -= rhs.value;
        }
    }
    impl<M: Mod, T: Into<Self>> MulAssign<T> for Fp<M> {
        fn mul_assign(&mut self, rhs: T) {
            self.value = reduce::<M>(u64::from(self.value) * u64::from(rhs.into().value));
        }
    }
    #[allow(clippy::suspicious_op_assign_impl)]
    impl<M: Mod, T: Into<Self>> DivAssign<T> for Fp<M> {
        fn div_assign(&mut self, rhs: T) {
            *self *= rhs.into().recip();
        }
    }
    impl<'a, M: Mod> From<&'a Self> for Fp<M> {
        fn from(x: &Self) -> Self {
            *x
        }
    }
    macro_rules! forward_ops {
        ($(($trait:ident, $method_assign:ident, $method:ident),)*) => {$(
            impl<M: Mod, T: Into<Fp<M>>> $trait<T> for Fp<M> {
                type Output = Self;
                fn $method(mut self, rhs: T) -> Self {
                    self.$method_assign(rhs);
                    self
                }
            }
            impl<'a, M: Mod, T: Into<Fp<M>>> $trait<T> for &'a Fp<M> {
                type Output = Fp<M>;
                fn $method(self, other: T) -> Self::Output {
                    $trait::$method(*self, other)
                }
            }
        )*};
    }
    forward_ops! {
        (Add, add_assign, add),
        (Sub, sub_assign, sub),
        (Mul, mul_assign, mul),
        (Div, div_assign, div),
    }
    impl<M: Mod> Neg for Fp<M> {
        type Output = Self;
        fn neg(self) -> Self {
            Self::from_raw(M::P * 2 - self.value)
        }
    }
    impl<M: Mod> Sum for Fp<M> {
        fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::new(0), |b, x| b + x)
        }
    }
    impl<M: Mod> Product for Fp<M> {
        fn product<I: Iterator<Item = Self>>(iter: I) -> Self {
            iter.fold(Self::new(1), |b, x| b * x)
        }
    }
    impl<'a, M: Mod> Sum<&'a Self> for Fp<M> {
        fn sum<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::new(0), |b, x| b + x)
        }
    }
    impl<'a, M: Mod> Product<&'a Self> for Fp<M> {
        fn product<I: Iterator<Item = &'a Self>>(iter: I) -> Self {
            iter.fold(Self::new(1), |b, x| b * x)
        }
    }
    impl<M: Mod> fmt::Debug for Fp<M> {
        fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> Result<(), std::fmt::Error> {
            let (num, den, _) = simplify(self.value() as i32, M::P as i32);
            let (num, den) = match den.signum() {
                1 => (num, den),
                -1 => (-num, -den),
                _ => unreachable!(),
            };
            if den == 1 {
                write!(f, "{}", num)
            } else {
                write!(f, "{}/{}", num, den)
            }
        }
    }
    impl<M: Mod> fmt::Display for Fp<M> {
        fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
            self.value().fmt(f)
        }
    }
}
// }}}
// erato {{{
#[allow(dead_code)]
mod erato {
    mod converters {
        use {
            super::{Int, PrimeFactorsByLookup, PrimeFactorsByTrialDivision},
            std::{iter::Peekable, marker::PhantomData},
        };
        pub trait PrimeFactors<T: Int>: Sized + Iterator<Item = T> {
            fn unique(self) -> Unique<T, Self> {
                Unique {
                    iter: self,
                    prev: None,
                }
            }
            fn rle(self) -> Rle<T, Self> {
                Rle {
                    iter: self.peekable(),
                    _marker: PhantomData,
                }
            }
        }
        impl<'a, T: Int> PrimeFactors<T> for PrimeFactorsByTrialDivision<'a, T> {}
        impl<'a, T: Int> PrimeFactors<T> for PrimeFactorsByLookup<'a, T> {}
        pub struct Unique<T: Int, P: PrimeFactors<T>> {
            iter: P,
            prev: Option<T>,
        }
        impl<T: Int, P: PrimeFactors<T>> Iterator for Unique<T, P> {
            type Item = P::Item;
            fn next(&mut self) -> Option<Self::Item> {
                let prev = self.prev;
                let res = self.iter.find(|&p| Some(p) != prev);
                self.prev = res;
                res
            }
        }
        pub struct Rle<T: Int, P: PrimeFactors<T>> {
            iter: Peekable<P>,
            _marker: PhantomData<T>,
        }
        impl<'a, T: Int, P: PrimeFactors<T>> Iterator for Rle<T, P> {
            type Item = (P::Item, usize);
            fn next(&mut self) -> Option<Self::Item> {
                if let Some(p) = self.iter.next() {
                    let mut multi = 1;
                    while self.iter.peek() == Some(&p) {
                        multi += 1;
                        self.iter.next();
                    }
                    Some((p, multi))
                } else {
                    None
                }
            }
        }
    }
    mod int {
        use std::{
            fmt::Debug,
            ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Rem, RemAssign, Sub, SubAssign},
        };
        pub trait Int:
            Debug
            + Copy
            + Ord
            + Add<Output = Self>
            + AddAssign
            + Sub<Output = Self>
            + SubAssign
            + Mul<Output = Self>
            + MulAssign
            + Div<Output = Self>
            + DivAssign
            + Rem<Output = Self>
            + RemAssign
        {
            fn zero() -> Self;
            fn one() -> Self;
            fn two() -> Self;
            fn as_usize(self) -> usize;
            fn from_usize(src: usize) -> Self;
        }
        macro_rules! impl_int {
            ($($t:ty),* $(,)?) => {$(
                impl Int for $t {
                    fn zero() -> Self {
                        0
                    }
                    fn one() -> Self {
                        1
                    }
                    fn two() -> Self {
                        2
                    }
                    fn as_usize(self) -> usize {
                        self as usize
                    }
                    fn from_usize(src: usize) -> Self {
                        src as Self
                    }
                }
            )*}
        }
        impl_int! {
            usize, u8, u16, u32, u64, u128,
            isize, i8, i16, i32, i64, i128,
        }
    }
    mod lpd_sieve {
        use super::{
            sieve_base::{PrimeFactorsByLookup, PrimeNumbers},
            sieve_kind, Int, SieveBase,
        };
        #[derive(Default, Debug, Clone, PartialEq)]
        pub struct LpdSieve {
            base: SieveBase<sieve_kind::Usize>,
        }
        impl LpdSieve {
            pub fn new() -> Self {
                Self {
                    base: SieveBase::new(),
                }
            }
            pub fn is_empty(&self) -> bool {
                self.base.is_empty()
            }
            pub fn len(&self) -> usize {
                self.base.len()
            }
            pub fn with_len(n: usize) -> Self {
                Self {
                    base: SieveBase::with_len(n),
                }
            }
            pub fn is_prime<T: Int>(&mut self, x: T) -> bool {
                self.base.is_prime(x)
            }
            pub fn lpd<T: Int>(&mut self, x: T) -> T {
                self.base.lpd(x)
            }
            pub fn prime_numbers<T: Int>(&mut self) -> PrimeNumbers<sieve_kind::Usize, T> {
                self.base.prime_numbers()
            }
            pub fn prime_factors<T: Int>(&mut self, n: T) -> PrimeFactorsByLookup<T> {
                self.base.prime_factors_by_lookup(n)
            }
        }
    }
    mod sieve {
        use super::{
            sieve_base::{PrimeFactorsByTrialDivision, PrimeNumbers},
            sieve_kind, Int, SieveBase,
        };
        #[derive(Default, Debug, Clone, PartialEq)]
        pub struct Sieve {
            base: SieveBase<sieve_kind::Boolean>,
        }
        impl Sieve {
            pub fn new() -> Self {
                Self {
                    base: SieveBase::new(),
                }
            }
            pub fn is_empty(&self) -> bool {
                self.base.is_empty()
            }
            pub fn len(&self) -> usize {
                self.base.len()
            }
            pub fn with_len(n: usize) -> Self {
                Self {
                    base: SieveBase::with_len(n),
                }
            }
            pub fn is_prime<T: Int>(&mut self, x: T) -> bool {
                self.base.is_prime(x)
            }
            pub fn prime_numbers<T: Int>(&mut self) -> PrimeNumbers<sieve_kind::Boolean, T> {
                self.base.prime_numbers()
            }
            pub fn prime_factors<T: Int>(&mut self, n: T) -> PrimeFactorsByTrialDivision<T> {
                self.base.prime_factors_by_trial_division(n)
            }
        }
    }
    mod sieve_base {
        use {
            super::{
                sieve_kind::{self, SieveKind},
                Int, PrimeFactors, Rle, Unique,
            },
            std::marker::PhantomData,
        };
        #[derive(Debug, Clone, PartialEq)]
        pub struct SieveBase<S: SieveKind> {
            sieve: Vec<S::SieveValue>,
            list: Vec<usize>,
        }
        impl<S: SieveKind> SieveBase<S> {
            pub fn new() -> Self {
                Self {
                    sieve: S::new(),
                    list: Vec::new(),
                }
            }
            pub fn is_empty(&self) -> bool {
                self.sieve.is_empty()
            }
            pub fn len(&self) -> usize {
                self.sieve.len()
            }
            pub fn with_len(n: usize) -> Self {
                let sieve = S::construct(n);
                let list = sieve
                    .iter()
                    .enumerate()
                    .filter(|&(index, &b)| S::is_prime(index, b))
                    .map(|(index, _)| index)
                    .collect();
                Self { sieve, list }
            }
            pub fn is_prime<T: Int>(&mut self, x: T) -> bool {
                assert!(T::zero() <= x);
                let x = x.as_usize();
                if self.sieve.len() <= x {
                    *self = Self::with_len(x + 1);
                }
                S::is_prime(x, self.sieve[x.as_usize()])
            }
            pub fn prime_numbers<T: Int>(&mut self) -> PrimeNumbers<S, T> {
                PrimeNumbers {
                    sieve: self,
                    index: 0,
                    _marker: PhantomData,
                }
            }
            fn extend(&mut self, len: usize) {
                assert!(2 * self.len() <= len);
                *self = Self::with_len(len);
            }
        }
        impl<S: SieveKind> Default for SieveBase<S> {
            fn default() -> Self {
                Self::new()
            }
        }
        impl SieveBase<sieve_kind::Boolean> {
            pub fn prime_factors_by_trial_division<T: Int>(
                &mut self,
                n: T,
            ) -> PrimeFactorsByTrialDivision<T> {
                assert!(T::zero() < n);
                let mut prime_numbers = self.prime_numbers();
                PrimeFactorsByTrialDivision {
                    p: prime_numbers.next().unwrap(),
                    prime_numbers,
                    n,
                }
            }
        }
        pub struct PrimeNumbers<'a, S: SieveKind, T: Int> {
            sieve: &'a mut SieveBase<S>,
            index: usize,
            _marker: PhantomData<T>,
        }
        pub struct PrimeFactorsByTrialDivision<'a, T: Int> {
            prime_numbers: PrimeNumbers<'a, sieve_kind::Boolean, T>,
            p: T,
            n: T,
        }
        impl<'a, S: SieveKind, T: Int> Iterator for PrimeNumbers<'a, S, T> {
            type Item = T;
            fn next(&mut self) -> Option<Self::Item> {
                let Self { sieve, index, .. } = self;
                let p = if let Some(&p) = sieve.list.get(*index) {
                    T::from_usize(p)
                } else {
                    sieve.extend((sieve.len() * 2).max(3));
                    T::from_usize(sieve.list[*index])
                };
                *index += 1;
                Some(p)
            }
        }
        impl<T: Int> PrimeFactorsByTrialDivision<'_, T> {
            pub fn unique(self) -> Unique<T, Self> {
                PrimeFactors::unique(self)
            }
            pub fn rle(self) -> Rle<T, Self> {
                PrimeFactors::rle(self)
            }
        }
        impl<'a, T: Int> Iterator for PrimeFactorsByTrialDivision<'a, T> {
            type Item = T;
            fn next(&mut self) -> Option<Self::Item> {
                let Self {
                    prime_numbers,
                    p,
                    n,
                } = self;
                if *n == T::one() {
                    None
                } else {
                    while *n % *p != T::zero() {
                        if *n <= *p * *p {
                            *p = *n;
                            break;
                        }
                        *p = prime_numbers.next().unwrap();
                    }
                    *n /= *p;
                    Some(*p)
                }
            }
        }
        pub struct PrimeFactorsByLookup<'a, T: Int> {
            sieve: &'a mut SieveBase<sieve_kind::Usize>,
            n: T,
        }
        impl SieveBase<sieve_kind::Usize> {
            pub fn prime_factors_by_lookup<T: Int>(&mut self, n: T) -> PrimeFactorsByLookup<T> {
                assert!(T::zero() < n);
                PrimeFactorsByLookup { sieve: self, n }
            }
            pub fn lpd<T: Int>(&mut self, n: T) -> T {
                let n = n.as_usize();
                if self.sieve.len() <= n {
                    self.extend(2 * (n + 1));
                }
                T::from_usize(self.sieve[n])
            }
        }
        impl<T: Int> PrimeFactorsByLookup<'_, T> {
            pub fn unique(self) -> Unique<T, Self> {
                PrimeFactors::unique(self)
            }
            pub fn rle(self) -> Rle<T, Self> {
                PrimeFactors::rle(self)
            }
        }
        impl<'a, T: Int> Iterator for PrimeFactorsByLookup<'a, T> {
            type Item = T;
            fn next(&mut self) -> Option<Self::Item> {
                let Self { sieve, n } = self;
                if *n == T::one() {
                    None
                } else {
                    let p = sieve.lpd(*n);
                    *n /= p;
                    Some(p)
                }
            }
        }
    }
    mod sieve_kind {
        pub trait SieveKind {
            type SieveValue: Copy;
            fn new() -> Vec<Self::SieveValue>;
            fn construct(len: usize) -> Vec<Self::SieveValue>;
            fn is_prime(index: usize, b: Self::SieveValue) -> bool;
        }
        #[derive(Debug, Clone, Copy, PartialEq)]
        pub enum Boolean {}
        #[derive(Debug, Clone, Copy, PartialEq)]
        pub enum Usize {}
        impl SieveKind for Boolean {
            type SieveValue = bool;
            fn new() -> Vec<Self::SieveValue> {
                Vec::new()
            }
            fn construct(len: usize) -> Vec<Self::SieveValue> {
                construct_is_prime_table(len)
            }
            fn is_prime(_index: usize, b: Self::SieveValue) -> bool {
                b
            }
        }
        impl SieveKind for Usize {
            type SieveValue = usize;
            fn new() -> Vec<Self::SieveValue> {
                Vec::new()
            }
            fn construct(len: usize) -> Vec<Self::SieveValue> {
                construct_lpd_table(len)
            }
            fn is_prime(index: usize, b: Self::SieveValue) -> bool {
                index == b
            }
        }
        pub fn construct_is_prime_table(n: usize) -> Vec<bool> {
            let mut is_prime = vec![true; n];
            (0..2.min(n)).for_each(|i| is_prime[i] = false);
            for p in (2..).take_while(|&p| p * p < n) {
                if !is_prime[p] {
                    continue;
                }
                let mut i = p * p;
                while i < n {
                    is_prime[i] = false;
                    i += p;
                }
            }
            is_prime
        }
        fn construct_lpd_table(n: usize) -> Vec<usize> {
            let mut lpd = vec![std::usize::MAX; n];
            for p in 2..n {
                if lpd[p] != std::usize::MAX {
                    continue;
                }
                lpd[p] = p;
                let mut i = p * p;
                while i < n {
                    if lpd[i] == std::usize::MAX {
                        lpd[i] = p;
                    }
                    i += p;
                }
            }
            lpd
        }
    }
    use sieve_base::SieveBase;
    pub use {
        converters::{PrimeFactors, Rle, Unique},
        int::Int,
        lpd_sieve::LpdSieve,
        sieve::Sieve,
        sieve_base::{PrimeFactorsByLookup, PrimeFactorsByTrialDivision, PrimeNumbers},
    };
}
// }}}
// template {{{
#[cfg(not(feature = "dbg"))]
#[allow(unused_macros)]
#[macro_export]
macro_rules! lg {
    ($($expr:expr),*) => {};
}

#[allow(dead_code)]
mod ngtio {

    mod i {
        use std::{
            io::{self, BufRead},
            iter,
        };

        pub use self::{
            multi_token::{Leaf, Parser, ParserTuple, RawTuple, Tuple, VecLen},
            token::{Token, Usize1},
        };

        pub fn with_stdin() -> Tokenizer<io::BufReader<io::Stdin>> {
            io::BufReader::new(io::stdin()).tokenizer()
        }

        pub fn with_str(src: &str) -> Tokenizer<&[u8]> {
            src.as_bytes().tokenizer()
        }

        pub struct Tokenizer<S: BufRead> {
            queue: Vec<String>, // FIXME: String のみにすると速そうです。
            scanner: S,
        }
        macro_rules! prim_method {
            ($name:ident: $T:ty) => {
                pub fn $name(&mut self) -> $T {
                    <$T>::leaf().parse(self)
                }
            };
            ($name:ident) => {
                prim_method!($name: $name);
            };
        }
        macro_rules! prim_methods {
            ($name:ident: $T:ty; $($rest:tt)*) => {
                prim_method!($name:$T);
                prim_methods!($($rest)*);
            };
            ($name:ident; $($rest:tt)*) => {
                prim_method!($name);
                prim_methods!($($rest)*);
            };
            () => ()
        }
        impl<S: BufRead> Tokenizer<S> {
            pub fn token(&mut self) -> String {
                self.load();
                self.queue.pop().expect("入力が終了したのですが。")
            }
            pub fn new(scanner: S) -> Self {
                Self {
                    queue: Vec::new(),
                    scanner,
                }
            }
            fn load(&mut self) {
                while self.queue.is_empty() {
                    let mut s = String::new();
                    let length = self.scanner.read_line(&mut s).unwrap(); // 入力が UTF-8 でないときにエラーだそうです。
                    if length == 0 {
                        break;
                    }
                    self.queue = s.split_whitespace().rev().map(str::to_owned).collect();
                }
            }

            pub fn skip_line(&mut self) {
                assert!(
                    self.queue.is_empty(),
                    "行の途中で呼ばないでいただきたいです。現在のトークンキュー: {:?}",
                    &self.queue
                );
                self.load();
            }

            pub fn end(&mut self) {
                self.load();
                assert!(self.queue.is_empty(), "入力はまだあります!");
            }

            pub fn parse<T: Token>(&mut self) -> T::Output {
                T::parse(&self.token())
            }

            pub fn parse_collect<T: Token, B>(&mut self, n: usize) -> B
            where
                B: iter::FromIterator<T::Output>,
            {
                iter::repeat_with(|| self.parse::<T>()).take(n).collect()
            }

            pub fn tuple<T: RawTuple>(&mut self) -> <T::LeafTuple as Parser>::Output {
                T::leaf_tuple().parse(self)
            }

            pub fn vec<T: Token>(&mut self, len: usize) -> Vec<T::Output> {
                T::leaf().vec(len).parse(self)
            }

            pub fn vec_tuple<T: RawTuple>(
                &mut self,
                len: usize,
            ) -> Vec<<T::LeafTuple as Parser>::Output> {
                T::leaf_tuple().vec(len).parse(self)
            }

            pub fn vec2<T: Token>(&mut self, height: usize, width: usize) -> Vec<Vec<T::Output>> {
                T::leaf().vec(width).vec(height).parse(self)
            }

            pub fn vec2_tuple<T>(
                &mut self,
                height: usize,
                width: usize,
            ) -> Vec<Vec<<T::LeafTuple as Parser>::Output>>
            where
                T: RawTuple,
            {
                T::leaf_tuple().vec(width).vec(height).parse(self)
            }
            prim_methods! {
                u8; u16; u32; u64; u128; usize;
                i8; i16; i32; i64; i128; isize;
                f32; f64;
                char; string: String;
            }
        }

        mod token {
            use super::multi_token::Leaf;
            use std::{any, fmt, marker, str};

            pub trait Token: Sized {
                type Output;
                fn parse(s: &str) -> Self::Output;
                fn leaf() -> Leaf<Self> {
                    Leaf(marker::PhantomData)
                }
            }

            impl<T> Token for T
            where
                T: str::FromStr,
                <T as str::FromStr>::Err: fmt::Debug,
            {
                type Output = T;
                fn parse(s: &str) -> Self::Output {
                    s.parse().unwrap_or_else(|_| {
                        panic!("Parse error!: ({}: {})", s, any::type_name::<T>(),)
                    })
                }
            }

            pub struct Usize1 {}
            impl Token for Usize1 {
                type Output = usize;
                fn parse(s: &str) -> Self::Output {
                    usize::parse(s)
                        .checked_sub(1)
                        .expect("Parse error! (Zero substruction error of Usize1)")
                }
            }
        }

        mod multi_token {
            use super::{Token, Tokenizer};
            use std::{io::BufRead, iter, marker};

            pub trait Parser: Sized {
                type Output;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output;
                fn vec(self, len: usize) -> VecLen<Self> {
                    VecLen { len, elem: self }
                }
            }
            pub struct Leaf<T>(pub(super) marker::PhantomData<T>);
            impl<T: Token> Parser for Leaf<T> {
                type Output = T::Output;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> T::Output {
                    server.parse::<T>()
                }
            }

            pub struct VecLen<T> {
                pub len: usize,
                pub elem: T,
            }
            impl<T: Parser> Parser for VecLen<T> {
                type Output = Vec<T::Output>;
                fn parse<S: BufRead>(&self, server: &mut Tokenizer<S>) -> Self::Output {
                    iter::repeat_with(|| self.elem.parse(server))
                        .take(self.len)
                        .collect()
                }
            }

            pub trait RawTuple {
                type LeafTuple: Parser;
                fn leaf_tuple() -> Self::LeafTuple;
            }
            pub trait ParserTuple {
                type Tuple: Parser;
                fn tuple(self) -> Self::Tuple;
            }
            pub struct Tuple<T>(pub T);
            macro_rules! impl_tuple {
                ($($t:ident: $T:ident),*) => {
                    impl<$($T),*> Parser for Tuple<($($T,)*)>
                        where
                            $($T: Parser,)*
                            {
                                type Output = ($($T::Output,)*);
#[allow(unused_variables)]
                                fn parse<S: BufRead >(&self, server: &mut Tokenizer<S>) -> Self::Output {
                                    match self {
                                        Tuple(($($t,)*)) => {
                                            ($($t.parse(server),)*)
                                        }
                                    }
                                }
                            }
                    impl<$($T: Token),*> RawTuple for ($($T,)*) {
                        type LeafTuple = Tuple<($(Leaf<$T>,)*)>;
                        fn leaf_tuple() -> Self::LeafTuple {
                            Tuple(($($T::leaf(),)*))
                        }
                    }
                    impl<$($T: Parser),*> ParserTuple for ($($T,)*) {
                        type Tuple = Tuple<($($T,)*)>;
                        fn tuple(self) -> Self::Tuple {
                            Tuple(self)
                        }
                    }
                };
            }
            impl_tuple!();
            impl_tuple!(t1: T1);
            impl_tuple!(t1: T1, t2: T2);
            impl_tuple!(t1: T1, t2: T2, t3: T3);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6);
            impl_tuple!(t1: T1, t2: T2, t3: T3, t4: T4, t5: T5, t6: T6, t7: T7);
            impl_tuple!(
                t1: T1,
                t2: T2,
                t3: T3,
                t4: T4,
                t5: T5,
                t6: T6,
                t7: T7,
                t8: T8
            );
        }

        trait Scanner: BufRead + Sized {
            fn tokenizer(self) -> Tokenizer<Self> {
                Tokenizer::new(self)
            }
        }
        impl<R: BufRead> Scanner for R {}
    }

    pub use self::i::{with_stdin, with_str};

    pub mod prelude {
        pub use super::i::{Parser, ParserTuple, RawTuple, Token, Usize1};
    }
}
// }}}
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