#791354 (Rust) No.8030 ミラー・ラビン素数判定法のテスト

• 問題: No.8030 ミラー・ラビン素数判定法のテスト
• ユーザー: 👑 Mizar
• 提出日時: 2022-08-21 18:15:42
• 言語: Rust (1.83.0 + proconio)
• 結果: AC
• 実行時間: 26 ms / 9,973 ms
• コード長: 20,218 bytes
• コンパイル時間: 13,496 ms
• コンパイル使用メモリ: 387,764 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-11-16 23:53:12
• 合計ジャッジ時間: 13,469 ms
• ジャッジサーバーID （参考情報）: judge1 / judge5

ファイルパターン	結果
other	AC * 10

ソースコード

// -*- coding:utf-8-unix -*-

use std::io::{BufRead,Write};

// https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8
#[allow(unused)]
macro_rules! input {
    ($($r:tt)*) => {
        let stdin = std::io::stdin();
        let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock()));
        let mut next = move || -> String{
            bytes.by_ref().map(|r|r.unwrap() as char)
                .skip_while(|c|c.is_whitespace())
                .take_while(|c|!c.is_whitespace())
                .collect()
        };
        input_inner!{next, $($r)*}
    };
}

#[allow(unused)]
macro_rules! input_inner {
    ($next:expr) => {};
    ($next:expr,) => {};
    ($next:expr, $var:ident : $t:tt $($r:tt)*) => {
        let $var = read_value!($next, $t);
        input_inner!{$next $($r)*}
    };
}

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

trait Change { fn chmax(&mut self, x: Self); fn chmin(&mut self, x: Self); }
impl<T: std::cmp::PartialOrd> Change for T {
    fn chmax(&mut self, x: T) { if *self < x { *self = x; } }
    fn chmin(&mut self, x: T) { if *self > x { *self = x; } }
}

// Integer Wrapper Traits
pub trait Zero { fn zero() -> Self; fn is_zero(&self) -> bool; }
pub trait One { fn one() -> Self; }
pub trait TrailingZeros { fn trailing_zeros(&self) -> u32; }
pub trait WrappingAdd { fn wrapping_add(&self, v: &Self) -> Self; }
pub trait WrappingSub { fn wrapping_sub(&self, v: &Self) -> Self; }
pub trait WrappingMul { fn wrapping_mul(&self, v: &Self) -> Self; }
pub trait WrappingNeg { fn wrapping_neg(&self) -> Self; }
pub trait IntNum:
    Copy
    + Eq
    + Ord
    + Zero
    + One
    + TrailingZeros
    + WrappingAdd
    + WrappingSub
    + WrappingMul
    + WrappingNeg
    + std::marker::Sized
    + std::ops::Add<Output = Self>
    + std::ops::AddAssign
    + std::ops::Sub<Output = Self>
    + std::ops::SubAssign
    + std::ops::Mul<Output = Self>
    + std::ops::Div<Output = Self>
    + std::ops::Rem<Output = Self>
    + std::ops::BitAnd<Output = Self>
    + std::ops::Shl<u32>
    + std::ops::ShlAssign<u32>
    + std::ops::Shr<u32>
    + std::ops::ShrAssign<u32>
    + std::fmt::Debug
{
}
pub trait UIntNum: IntNum {}
pub trait IIntNum: IntNum {}
macro_rules! define_zero_one {
    ($ty:ty, $zero:expr, $one:expr) => {
        impl Zero for $ty {
            #[inline]
            fn zero() -> Self {
                $zero
            }
            #[inline]
            fn is_zero(&self) -> bool {
                *self == $zero
            }
        }
        impl One for $ty {
            #[inline]
            fn one() -> Self {
                $one
            }
        }
    };
}
define_zero_one!(usize, 0, 1);
define_zero_one!(u8, 0, 1);
define_zero_one!(u16, 0, 1);
define_zero_one!(u32, 0, 1);
define_zero_one!(u64, 0, 1);
define_zero_one!(u128, 0, 1);
define_zero_one!(isize, 0, 1);
define_zero_one!(i8, 0, 1);
define_zero_one!(i16, 0, 1);
define_zero_one!(i32, 0, 1);
define_zero_one!(i64, 0, 1);
define_zero_one!(i128, 0, 1);
define_zero_one!(f32, 0.0, 1.0);
define_zero_one!(f64, 0.0, 1.0);
macro_rules! integer_bitcount_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self) -> u32 {
                <$t>::$method(*self)
            }
        }
    };
}
macro_rules! integer_wrapping_impl {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self, v: &Self) -> Self {
                <$t>::$method(*self, *v)
            }
        }
    };
    ($trait_name:ident, $method:ident, $t:ty, $rhs:ty) => {
        impl $trait_name<$rhs> for $t {
            #[inline]
            fn $method(&self, v: &$rhs) -> Self {
                <$t>::$method(*self, *v)
            }
        }
    };
}
macro_rules! integer_wrapping_impl1 {
    ($trait_name:ident, $method:ident, $t:ty) => {
        impl $trait_name for $t {
            #[inline]
            fn $method(&self) -> Self {
                <$t>::$method(*self)
            }
        }
    };
}
integer_bitcount_impl!(TrailingZeros, trailing_zeros, u8);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, u16);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, u32);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, u64);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, u128);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, usize);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, i8);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, i16);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, i32);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, i64);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, i128);
integer_bitcount_impl!(TrailingZeros, trailing_zeros, isize);
integer_wrapping_impl!(WrappingAdd, wrapping_add, u8);
integer_wrapping_impl!(WrappingAdd, wrapping_add, u16);
integer_wrapping_impl!(WrappingAdd, wrapping_add, u32);
integer_wrapping_impl!(WrappingAdd, wrapping_add, u64);
integer_wrapping_impl!(WrappingAdd, wrapping_add, u128);
integer_wrapping_impl!(WrappingAdd, wrapping_add, usize);
integer_wrapping_impl!(WrappingAdd, wrapping_add, i8);
integer_wrapping_impl!(WrappingAdd, wrapping_add, i16);
integer_wrapping_impl!(WrappingAdd, wrapping_add, i32);
integer_wrapping_impl!(WrappingAdd, wrapping_add, i64);
integer_wrapping_impl!(WrappingAdd, wrapping_add, i128);
integer_wrapping_impl!(WrappingAdd, wrapping_add, isize);
integer_wrapping_impl!(WrappingSub, wrapping_sub, u8);
integer_wrapping_impl!(WrappingSub, wrapping_sub, u16);
integer_wrapping_impl!(WrappingSub, wrapping_sub, u32);
integer_wrapping_impl!(WrappingSub, wrapping_sub, u64);
integer_wrapping_impl!(WrappingSub, wrapping_sub, u128);
integer_wrapping_impl!(WrappingSub, wrapping_sub, usize);
integer_wrapping_impl!(WrappingSub, wrapping_sub, i8);
integer_wrapping_impl!(WrappingSub, wrapping_sub, i16);
integer_wrapping_impl!(WrappingSub, wrapping_sub, i32);
integer_wrapping_impl!(WrappingSub, wrapping_sub, i64);
integer_wrapping_impl!(WrappingSub, wrapping_sub, i128);
integer_wrapping_impl!(WrappingSub, wrapping_sub, isize);
integer_wrapping_impl!(WrappingMul, wrapping_mul, u8);
integer_wrapping_impl!(WrappingMul, wrapping_mul, u16);
integer_wrapping_impl!(WrappingMul, wrapping_mul, u32);
integer_wrapping_impl!(WrappingMul, wrapping_mul, u64);
integer_wrapping_impl!(WrappingMul, wrapping_mul, u128);
integer_wrapping_impl!(WrappingMul, wrapping_mul, usize);
integer_wrapping_impl!(WrappingMul, wrapping_mul, i8);
integer_wrapping_impl!(WrappingMul, wrapping_mul, i16);
integer_wrapping_impl!(WrappingMul, wrapping_mul, i32);
integer_wrapping_impl!(WrappingMul, wrapping_mul, i64);
integer_wrapping_impl!(WrappingMul, wrapping_mul, i128);
integer_wrapping_impl!(WrappingMul, wrapping_mul, isize);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, u8);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, u16);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, u32);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, u64);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, u128);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, usize);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, i8);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, i16);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, i32);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, i64);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, i128);
integer_wrapping_impl1!(WrappingNeg, wrapping_neg, isize);
impl IntNum for usize {}
impl IntNum for u8 {}
impl IntNum for u16 {}
impl IntNum for u32 {}
impl IntNum for u64 {}
impl IntNum for u128 {}
impl IntNum for isize {}
impl IntNum for i8 {}
impl IntNum for i16 {}
impl IntNum for i32 {}
impl IntNum for i64 {}
impl IntNum for i128 {}
impl UIntNum for usize {}
impl UIntNum for u8 {}
impl UIntNum for u16 {}
impl UIntNum for u32 {}
impl UIntNum for u64 {}
impl UIntNum for u128 {}
impl IIntNum for isize {}
impl IIntNum for i8 {}
impl IIntNum for i16 {}
impl IIntNum for i32 {}
impl IIntNum for i64 {}
impl IIntNum for i128 {}

// モンゴメリ剰余乗算 (Montgomery modular multiplication)
pub trait UMontTrait<T: UIntNum> {
    fn m(&self) -> T;
    fn mi(&self) -> T;
    fn tr(&self) -> T;
    fn tr2(&self) -> T;
    #[inline]
    fn d(&self) -> T {
        let mut d = self.m() - T::one();
        let k = d.trailing_zeros();
        d >>= k;
        d
    }
    #[inline]
    fn k(&self) -> u32 {
        let d = self.m() - T::one();
        let k = d.trailing_zeros();
        k
    }
    fn new(m: T) -> Self;
    fn mrmul(&self, ar: T, br: T) -> T;
    fn mr(&self, ar: T) -> T;
    #[inline]
    fn ar(&self, a: T) -> T {
        // == a * r (mod m)
        debug_assert!(a < self.m());
        self.mrmul(a, self.tr2())
    }
    #[inline]
    fn powir(&self, mut ar: T, mut b: T) -> T {
        // == ((ar / r) ** b) * r (mod m)
        debug_assert!(ar < self.m());
        let mut t = if (b & T::one()).is_zero() { self.tr() } else { ar };
        b >>= 1;
        while !b.is_zero() {
            ar = self.mrmul(ar, ar);
            t = self.mrmul(t, if (b & T::one()).is_zero() { self.tr() } else { ar });
            b >>= 1;
        }
        t
    }
    fn prime_test_once(&self, base: T) -> bool {
        // Miller-Rabin primality test
        debug_assert!(base > T::one());
        let (m, r, d, k) = (self.m(), self.tr(), self.d(), self.k());
        let b = base % m;
        if b.is_zero() { return true; }
        let mut br = self.powir(self.ar(b), d);
        if br == r { return true; }
        let negr = m - r;
        for _ in 0..k {
            if br == negr { return true; }
            br = self.mrmul(br, br);
        }
        false
    }
}
pub struct U64Mont {
    m: u64, // m is odd, and m > 2
    mi: u64, // m * mi == 1 (mod 2**64)
    r: u64, // == 2**64 (mod m)
    r2: u64, // == 2**128 (mod m)
    d: u64, // == (m - 1) >> (m - 1).trailing_zeros()
    k: u32, // == (m - 1).trailing_zeros()
}
impl UMontTrait<u64> for U64Mont {
    #[inline] fn m(&self) -> u64 { self.m }
    #[inline] fn mi(&self) -> u64 { self.mi }
    #[inline] fn tr(&self) -> u64 { self.r }
    #[inline] fn tr2(&self) -> u64 { self.r2 }
    #[inline] fn d(&self) -> u64 { self.d }
    #[inline] fn k(&self) -> u32 { self.k }
    #[inline]
    fn new(m: u64) -> Self {
        debug_assert_eq!(m & 1, 1);
        // // m is odd number, m = 2*k+1, m >= 1, m < 2**64, k is non-negative integer, k >= 0, k < 2**63
        // mi0 := m; // = 2*k+1 = (1+(2**2)*((k*(k+1))**1))/(2*k+1)
        let mut mi = m;
        // mi1 := mi0 * (2 - (m * mi0)); // = (1-(2**4)*((k*(k+1))**2))/(2*k+1)
        // mi2 := mi1 * (2 - (m * mi1)); // = (1-(2**8)*((k*(k+1))**4))/(2*k+1)
        // mi3 := mi2 * (2 - (m * mi2)); // = (1-(2**16)*((k*(k+1))**8))/(2*k+1)
        // mi4 := mi3 * (2 - (m * mi3)); // = (1-(2**32)*((k*(k+1))**16))/(2*k+1)
        // mi5 := mi4 * (2 - (m * mi4)); // = (1-(2**64)*((k*(k+1))**32))/(2*k+1)
        // // (m * mi5) mod 2**64 = ((2*k+1) * mi5) mod 2**64 = 1 mod 2**64
        for _ in 0..5 {
            mi = mi.wrapping_mul(2u64.wrapping_sub(m.wrapping_mul(mi)));
        }
        debug_assert_eq!(m.wrapping_mul(mi), 1); // m * mi == 1 (mod 2**64)
        let r: u64 = m.wrapping_neg() % m; // == 2**64 (mod m)
        let r2: u64 = ((m as u128).wrapping_neg() % (m as u128)) as u64; // == 2**128 (mod m)
        let mut d = m - 1;
        let k = d.trailing_zeros();
        d >>= k;
        debug_assert_eq!(Self { m, mi, r, r2, d, k }.mr(r), 1); // r / r == 1 (mod m)
        debug_assert_eq!(Self { m, mi, r, r2, d, k }.mrmul(1, r2), r); // r2 / r == r (mod m)
        Self { m, mi, r, r2, d, k }
    }
    #[inline]
    fn mrmul(&self, ar: u64, br: u64) -> u64 {
        // == (ar * br) / r (mod m)
        debug_assert!(ar < self.m);
        debug_assert!(br < self.m);
        let (m, mi) = (self.m, self.mi);
        let t: u128 = (ar as u128) * (br as u128);
        let t: (u64, bool) = ((t >> 64) as u64).overflowing_sub((((((t as u64).wrapping_mul(mi)) as u128) * (m as u128)) >> 64) as u64);
        if t.1 { t.0.wrapping_add(m) } else { t.0 }
    }
    #[inline]
    fn mr(&self, ar: u64) -> u64 {
        // == ar / r (mod m)
        debug_assert!(ar < self.m);
        let (m, mi) = (self.m, self.mi);
        let t: (u64, bool) = (((((ar.wrapping_mul(mi)) as u128) * (m as u128)) >> 64) as u64).overflowing_neg();
        if t.1 { t.0.wrapping_add(m) } else { t.0 }
    }
}
pub struct U32Mont {
    m: u32, // m is odd, and m > 2
    mi: u32, // m * mi == 1 (mod 2**32)
    r: u32, // == 2**32 (mod m)
    r2: u32, // == 2**64 (mod m)
    d: u32, // == (m - 1) >> (m - 1).trailing_zeros()
    k: u32, // == (m - 1).trailing_zeros()
}
impl UMontTrait<u32> for U32Mont {
    #[inline] fn m(&self) -> u32 { self.m }
    #[inline] fn mi(&self) -> u32 { self.mi }
    #[inline] fn tr(&self) -> u32 { self.r }
    #[inline] fn tr2(&self) -> u32 { self.r2 }
    #[inline] fn d(&self) -> u32 { self.d }
    #[inline] fn k(&self) -> u32 { self.k }
    #[inline]
    fn new(m: u32) -> Self {
        debug_assert_eq!(m & 1, 1);
        // // m is odd number, m = 2*k+1, m >= 1, m < 2**64, k is non-negative integer, k >= 0, k < 2**63
        // mi0 := m; // = 2*k+1 = (1+(2**2)*((k*(k+1))**1))/(2*k+1)
        let mut mi = m;
        // mi1 := mi0 * (2 - (m * mi0)); // = (1-(2**4)*((k*(k+1))**2))/(2*k+1)
        // mi2 := mi1 * (2 - (m * mi1)); // = (1-(2**8)*((k*(k+1))**4))/(2*k+1)
        // mi3 := mi2 * (2 - (m * mi2)); // = (1-(2**16)*((k*(k+1))**8))/(2*k+1)
        // mi4 := mi3 * (2 - (m * mi3)); // = (1-(2**32)*((k*(k+1))**16))/(2*k+1)
        // // (m * mi4) mod 2**32 = ((2*k+1) * mi4) mod 2**32 = 1 mod 2**32
        for _ in 0..4 {
            mi = mi.wrapping_mul(2u32.wrapping_sub(m.wrapping_mul(mi)));
        }
        debug_assert_eq!(m.wrapping_mul(mi), 1); // m * mi == 1 (mod 2**32)
        let r: u32 = m.wrapping_neg() % m; // == 2**64 (mod m)
        let r2: u32 = ((m as u64).wrapping_neg() % (m as u64)) as u32; // == 2**64 (mod m)
        let mut d = m - 1;
        let k = d.trailing_zeros();
        d >>= k;
        debug_assert_eq!(Self { m, mi, r, r2, d, k }.mr(r), 1); // r / r == 1 (mod m)
        debug_assert_eq!(Self { m, mi, r, r2, d, k }.mrmul(1, r2), r); // r2 / r == r (mod m)
        Self { m, mi, r, r2, d, k }
    }
    #[inline]
    fn mrmul(&self, ar: u32, br: u32) -> u32 {
        // == (ar * br) / r (mod m)
        debug_assert!(ar < self.m);
        debug_assert!(br < self.m);
        let (m, mi) = (self.m, self.mi);
        let t: u64 = (ar as u64) * (br as u64);
        let t: (u32, bool) = ((t >> 32) as u32).overflowing_sub((((((t as u32).wrapping_mul(mi)) as u64) * (m as u64)) >> 32) as u32);
        if t.1 { t.0.wrapping_add(m) } else { t.0 }
    }
    #[inline]
    fn mr(&self, ar: u32) -> u32 {
        // == ar / r (mod m)
        debug_assert!(ar < self.m);
        let (m, mi) = (self.m, self.mi);
        let t: (u32, bool) = (((((ar.wrapping_mul(mi)) as u64) * (m as u64)) >> 32) as u32).overflowing_neg();
        if t.1 { t.0.wrapping_add(m) } else { t.0 }
    }
}

pub fn prime_test_32(m: u32) -> bool {
    if m == 2 { return true; }
    if m == 1 || (m & 1) == 0 { return false; }
    let u32mont = U32Mont::new(m);
    match m {
        // Deterministic variants of the Miller-Rabin primality test
        // http://miller-rabin.appspot.com/
        0..=49141 => {
            u32mont.prime_test_once(921211727)
        },
        0..=360018361 => {
            u32mont.prime_test_once(1143370) &&
            u32mont.prime_test_once(2350307676)
        },
        _ => {
            u32mont.prime_test_once(2) &&
            u32mont.prime_test_once(7) &&
            u32mont.prime_test_once(61)
        }
    }
}
pub fn prime_test_64(m: u64) -> bool {
    if m == 2 { return true; }
    if m == 1 || (m & 1) == 0 { return false; }
    let u64mont = U64Mont::new(m);
    match m {
        // Deterministic variants of the Miller-Rabin primality test
        // http://miller-rabin.appspot.com/
        0..=341531 => {
            u64mont.prime_test_once(9345883071009581737)
        },
        0..=1050535501 => {
            u64mont.prime_test_once(336781006125) &&
            u64mont.prime_test_once(9639812373923155)
        },
        0..=350269456337 => {
            u64mont.prime_test_once(4230279247111683200) &&
            u64mont.prime_test_once(14694767155120705706) &&
            u64mont.prime_test_once(16641139526367750375)
        },
        0..=55245642489451 => {
            u64mont.prime_test_once(2) &&
            u64mont.prime_test_once(141889084524735) &&
            u64mont.prime_test_once(1199124725622454117) &&
            u64mont.prime_test_once(11096072698276303650)
        },
        0..=7999252175582851 => {
            u64mont.prime_test_once(2) &&
            u64mont.prime_test_once(4130806001517) &&
            u64mont.prime_test_once(149795463772692060) &&
            u64mont.prime_test_once(186635894390467037) &&
            u64mont.prime_test_once(3967304179347715805)
        },
        0..=585226005592931977 => {
            u64mont.prime_test_once(2) &&
            u64mont.prime_test_once(123635709730000) &&
            u64mont.prime_test_once(9233062284813009) &&
            u64mont.prime_test_once(43835965440333360) &&
            u64mont.prime_test_once(761179012939631437) &&
            u64mont.prime_test_once(1263739024124850375)
        },
        _ => {
            u64mont.prime_test_once(2) &&
            u64mont.prime_test_once(325) &&
            u64mont.prime_test_once(9375) &&
            u64mont.prime_test_once(28178) &&
            u64mont.prime_test_once(450775) &&
            u64mont.prime_test_once(9780504) &&
            u64mont.prime_test_once(1795265022)
        },
    }
}
pub fn prime_test_64_f(m: u64) -> bool {
    if m == 2 { return true; }
    if m == 1 || (m & 1) == 0 { return false; }
    let u64mont = U64Mont::new(m);
    u64mont.prime_test_once(2) &&
    u64mont.prime_test_once(325) &&
    u64mont.prime_test_once(9375) &&
    u64mont.prime_test_once(28178) &&
    u64mont.prime_test_once(450775) &&
    u64mont.prime_test_once(9780504) &&
    u64mont.prime_test_once(1795265022)
}

fn main() {
    let start_time = std::time::Instant::now();
    let out = std::io::stdout();
    let mut out = std::io::BufWriter::new(out.lock());
    macro_rules! puts {($($format:tt)*) => (let _ = write!(out,$($format)*););}
    /*
    input! {
        n: usize,
        x: [u64; n],
    }
    */
    let input = std::io::stdin();
    let mut lines = std::io::BufReader::new(input.lock()).lines();
    let n: usize = lines.next().unwrap().unwrap().parse().unwrap();
    /*
    let x: Vec<u64> = lines.take(n).map(|l| l.unwrap().parse().unwrap()).collect();
    let elapsed1 = start_time.elapsed();
    let res: Vec<bool> = x.iter().map(|&v| prime_test_64_f(v)).collect();
    let elapsed2 = start_time.elapsed();
    for i in 0..n {
        puts!("{} {}\n", x[i], if res[i] { "1" } else { "0" });
    }
    let elapsed3 = start_time.elapsed();
    out.flush().unwrap();
    let elapsed4 = start_time.elapsed();
    eprint!(
        "  input: {}us\ncompute: {}us\n output: {}us\n wflush: {}us\n",
        elapsed1.as_micros(),
        elapsed2.as_micros(),
        elapsed3.as_micros(),
        elapsed4.as_micros(),
    );
    */
    for _ in 0..n {
        let x: u64 = lines.next().unwrap().unwrap().parse().unwrap();
        puts!("{} {}\n", x, if prime_test_64_f(x) { "1" } else { "0" });
    }
    let elapsed = start_time.elapsed();
    eprint!("{}us\n", elapsed.as_micros());
}