#575695 (Rust) No.1275 綺麗な式

• 問題: No.1275 綺麗な式
• ユーザー: cotton_fn_
• 提出日時: 2020-11-04 23:25:53
• 言語: Rust (1.77.0 + proconio)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 9,571 bytes
• コンパイル時間: 13,347 ms
• コンパイル使用メモリ: 386,920 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-07-22 10:28:50
• 合計ジャッジ時間: 15,414 ms
• ジャッジサーバーID （参考情報）: judge4 / judge1

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	1 ms; 5,248 KB
testcase_02	AC	1 ms; 5,376 KB
testcase_03	AC	2 ms; 5,376 KB
testcase_04	AC	1 ms; 5,376 KB
testcase_05	AC	1 ms; 5,376 KB
testcase_06	AC	1 ms; 5,376 KB
testcase_07	AC	1 ms; 5,376 KB
testcase_08	AC	1 ms; 5,376 KB
testcase_09	AC	1 ms; 5,376 KB
testcase_10	AC	1 ms; 5,376 KB
testcase_11	AC	1 ms; 5,376 KB
testcase_12	AC	1 ms; 5,376 KB
testcase_13	AC	1 ms; 5,376 KB
testcase_14	AC	1 ms; 5,376 KB
testcase_15	AC	2 ms; 5,376 KB
testcase_16	AC	1 ms; 5,376 KB
testcase_17	AC	1 ms; 5,376 KB
testcase_18	AC	1 ms; 5,376 KB
testcase_19	AC	1 ms; 5,376 KB
testcase_20	AC	1 ms; 5,376 KB
testcase_21	AC	1 ms; 5,376 KB
testcase_22	AC	1 ms; 5,376 KB
testcase_23	AC	1 ms; 5,376 KB
testcase_24	AC	2 ms; 5,376 KB
testcase_25	AC	1 ms; 5,376 KB
testcase_26	AC	1 ms; 5,376 KB
testcase_27	AC	1 ms; 5,376 KB
testcase_28	AC	1 ms; 5,376 KB
testcase_29	AC	1 ms; 5,376 KB
testcase_30	AC	1 ms; 5,376 KB
testcase_31	AC	1 ms; 5,376 KB
testcase_32	AC	1 ms; 5,376 KB
testcase_33	AC	1 ms; 5,376 KB
testcase_34	AC	1 ms; 5,376 KB
testcase_35	AC	2 ms; 5,376 KB
testcase_36	AC	1 ms; 5,376 KB
testcase_37	AC	1 ms; 5,376 KB
testcase_38	AC	1 ms; 5,376 KB
testcase_39	AC	1 ms; 5,376 KB
testcase_40	AC	1 ms; 5,376 KB
testcase_41	AC	1 ms; 5,376 KB
testcase_42	AC	1 ms; 5,376 KB
testcase_43	AC	1 ms; 5,376 KB
testcase_44	AC	1 ms; 5,376 KB
testcase_45	AC	1 ms; 5,376 KB
testcase_46	AC	1 ms; 5,376 KB
testcase_47	AC	1 ms; 5,376 KB
testcase_48	AC	1 ms; 5,376 KB
testcase_49	AC	1 ms; 5,376 KB
testcase_50	AC	1 ms; 5,376 KB
testcase_51	AC	1 ms; 5,376 KB
testcase_52	AC	1 ms; 5,376 KB
testcase_53	AC	1 ms; 5,376 KB
testcase_54	AC	2 ms; 5,376 KB
testcase_55	AC	1 ms; 5,376 KB
testcase_56	AC	1 ms; 5,376 KB
testcase_57	AC	1 ms; 5,376 KB
testcase_58	AC	1 ms; 5,376 KB
testcase_59	AC	1 ms; 5,376 KB
testcase_60	AC	1 ms; 5,376 KB
testcase_61	AC	1 ms; 5,376 KB

ソースコード

#![allow(unused_imports, unused_macros)]

use kyoproio::*;
use std::{
    collections::*,
    io::{self, prelude::*},
    iter,
    mem::{replace, swap},
};

fn run<I: Input, O: Write>(mut kin: I, mut out: O) {
    macro_rules! output { ($($args:expr),+) => { write!(&mut out, $($args),+).unwrap(); }; }
    macro_rules! outputln {
        ($($args:expr),+) => { output!($($args),+); outputln!(); };
        () => { output!("\n"); if cfg!(debug_assertions) { out.flush().unwrap(); } }
    }

    let (a, b, n): (i32, i32, u64) = kin.input();
    let a = mint(a);
    let b = mint(b);
    // (x, y): x + y * sqrt(b)
    let id = (mint(1), mint(0));
    type Mint = ModInt<Mod1e9p7>;
    type P = (Mint, Mint);
    let f = |&(x1, y1): &P, &(x2, y2): &P| (x1 * x2 + b * y1 * y2, x1 * y2 + x2 * y1); 
    let (s1, t1) = pow((a, mint(1)), n, id, f);
    let (s2, t2) = pow((a, -mint(1)), n, id, f);
    assert_eq!(t1, -t2);
    outputln!("{}", s1 + s2);
}

pub fn pow<T, F: Fn(&T, &T) -> T>(mut x: T, mut k: u64, init: T, f: F) -> T {
    let mut y = init;
    while k > 0 {
        if k & 1 == 1 {
            y = f(&x, &y);
        }
        x = f(&x, &x);
        k >>= 1;
    }
    y
}

fn mint<T: Into<i32>>(x: T) -> ModInt<Mod1e9p7> {
    ModInt::new(x.into(), Mod1e9p7)
}
pub trait Modulo: Copy {
    fn modulo(&self) -> i32;
}
#[derive(Copy, Clone, Eq, PartialEq)]
struct Mod998244353;
impl Modulo for Mod998244353 {
    fn modulo(&self) -> i32 {
        998244353
    }
}
#[derive(Copy, Clone, Eq, PartialEq)]
struct Mod1e9p7;
impl Modulo for Mod1e9p7 {
    fn modulo(&self) -> i32 {
        1e9 as i32 + 7
    }
}
#[derive(Copy, Clone, Eq, PartialEq)]
struct VarMod(i32);
impl Modulo for VarMod {
    fn modulo(&self) -> i32 {
        self.0
    }
}
use std::{fmt, ops};
#[derive(Copy, Clone, Eq, PartialEq)]
pub struct ModInt<M>(i32, M);
impl<M: Modulo> ModInt<M> {
    pub fn new(x: i32, m: M) -> Self {
        debug_assert!(x < m.modulo());
        Self(x, m)
    }
    pub fn value(&self) -> i32 {
        self.0
    }
    pub fn inv(&self) -> Self {
        self.pow((self.m() - 2) as u64)
    }
    pub fn pow(&self, mut n: u64) -> Self {
        let mut x = *self;
        let mut y = Self(1, self.1);
        while n > 0 {
            if n & 1 == 1 {
                y *= x;
            }
            x *= x;
            n >>= 1;
        }
        y
    }
    pub fn half(&self) -> Self {
        Self(self.0 / 2 + self.0 % 2 * ((self.m() + 1) / 2), self.1)
    }
    fn m(&self) -> i32 {
        self.1.modulo()
    }
}
impl<M: Modulo> ops::Neg for ModInt<M> {
    type Output = Self;
    fn neg(self) -> Self {
        Self(if self.0 == 0 { 0 } else { self.m() - self.0 }, self.1)
    }
}
impl<M: Modulo> ops::AddAssign for ModInt<M> {
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
        if self.0 >= self.m() {
            self.0 -= self.m();
        }
    }
}
impl<M: Modulo> ops::SubAssign for ModInt<M> {
    fn sub_assign(&mut self, rhs: Self) {
        self.0 -= rhs.0;
        if self.0 < 0 {
            self.0 += self.m();
        }
    }
}
impl<M: Modulo> ops::MulAssign for ModInt<M> {
    fn mul_assign(&mut self, rhs: Self) {
        self.0 = (self.0 as u32 as u64 * rhs.0 as u32 as u64 % self.m() as u32 as u64) as i32;
    }
}
impl<M: Modulo> ops::DivAssign for ModInt<M> {
    fn div_assign(&mut self, rhs: Self) {
        assert_ne!(rhs.value(), 0);
        *self *= rhs.inv();
    }
}
macro_rules! op_impl {
    ($($Op:ident $op:ident $OpAssign:ident $op_assign:ident)*) => {
        $(impl<M: Modulo> ops::$Op for ModInt<M> {
            type Output = Self;
            fn $op(self, rhs: Self) -> Self {
                let mut res = self;
                ops::$OpAssign::$op_assign(&mut res, rhs);
                res
            }
        })*
    };
}
op_impl! {
    Add add AddAssign add_assign
    Sub sub SubAssign sub_assign
    Mul mul MulAssign mul_assign
    Div div DivAssign div_assign
}
impl<M: Modulo> fmt::Display for ModInt<M> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        self.0.fmt(f)
    }
}
impl<M: Modulo> fmt::Debug for ModInt<M> {
    fn fmt(&self, f: &mut fmt::Formatter<'_>) -> fmt::Result {
        f.pad("ModInt(")?;
        self.0.fmt(f)?;
        f.pad(")")
    }
}

// -----------------------------------------------------------------------------
fn main() -> io::Result<()> {
    std::thread::Builder::new()
        .stack_size(64 * 1024 * 1024)
        .spawn(|| {
            run(
                KInput::new(io::stdin().lock()),
                io::BufWriter::new(io::stdout().lock()),
            )
        })?
        .join()
        .unwrap();
    Ok(())
}

// -----------------------------------------------------------------------------
pub mod kyoproio {
    use std::io::prelude::*;
    pub trait Input {
        fn bytes(&mut self) -> &[u8];
        fn str(&mut self) -> &str {
            std::str::from_utf8(self.bytes()).unwrap()
        }
        fn input<T: InputParse>(&mut self) -> T {
            T::input(self)
        }
        fn iter<T: InputParse>(&mut self) -> Iter<T, Self> {
            Iter(self, std::marker::PhantomData)
        }
        fn seq<T: InputParse, B: std::iter::FromIterator<T>>(&mut self, n: usize) -> B {
            self.iter().take(n).collect()
        }
    }
    pub struct KInput<R> {
        src: R,
        buf: Vec<u8>,
        pos: usize,
        len: usize,
    }
    impl<R: Read> KInput<R> {
        pub fn new(src: R) -> Self {
            Self {
                src,
                buf: vec![0; 1 << 16],
                pos: 0,
                len: 0,
            }
        }
    }
    impl<R: Read> Input for KInput<R> {
        fn bytes(&mut self) -> &[u8] {
            loop {
                while let Some(delim) = self.buf[self.pos..self.len]
                    .iter()
                    .position(|b| b.is_ascii_whitespace())
                {
                    let range = self.pos..self.pos + delim;
                    self.pos += delim + 1;
                    if delim > 0 {
                        return &self.buf[range];
                    }
                }
                if self.pos > 0 {
                    self.buf.copy_within(self.pos..self.len, 0);
                    self.len -= self.pos;
                    self.pos = 0;
                }
                if self.len >= self.buf.len() {
                    self.buf.resize(2 * self.buf.len(), 0);
                }
                let read = self.src.read(&mut self.buf[self.len..]).unwrap();
                if read == 0 {
                    let range = self.pos..self.len;
                    self.pos = self.len;
                    return &self.buf[range];
                }
                self.len += read;
            }
        }
    }
    pub struct Iter<'a, T, I: ?Sized>(&'a mut I, std::marker::PhantomData<*const T>);
    impl<'a, T: InputParse, I: Input + ?Sized> Iterator for Iter<'a, T, I> {
        type Item = T;
        fn next(&mut self) -> Option<T> {
            Some(self.0.input())
        }
    }
    pub trait InputParse: Sized {
        fn input<I: Input + ?Sized>(src: &mut I) -> Self;
    }
    impl InputParse for Vec<u8> {
        fn input<I: Input + ?Sized>(src: &mut I) -> Self {
            src.bytes().to_owned()
        }
    }
    macro_rules! from_str_impl {
        { $($T:ty)* } => {
            $(impl InputParse for $T {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    src.str().parse::<$T>().unwrap()
                }
            })*
        }
    }
    from_str_impl! { String char bool f32 f64 }
    macro_rules! parse_int_impl {
        { $($I:ty: $U:ty)* } => {
            $(impl InputParse for $I {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    let f = |s: &[u8]| s.iter().fold(0, |x, b| 10 * x + (b & 0xf) as $I);
                    let s = src.bytes();
                    if let Some((&b'-', t)) = s.split_first() { -f(t) } else { f(s) }
                }
            }
            impl InputParse for $U {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    src.bytes().iter().fold(0, |x, b| 10 * x + (b & 0xf) as $U)
                }
            })*
        };
    }
    parse_int_impl! { isize:usize i8:u8 i16:u16 i32:u32 i64:u64 i128:u128 }
    macro_rules! tuple_impl {
        ($H:ident $($T:ident)*) => {
            impl<$H: InputParse, $($T: InputParse),*> InputParse for ($H, $($T),*) {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    ($H::input(src), $($T::input(src)),*)
                }
            }
            tuple_impl!($($T)*);
        };
        () => {}
    }
    tuple_impl!(A B C D E F G);
    macro_rules! array_impl {
        { $($N:literal)* } => {
            $(impl<T: InputParse> InputParse for [T; $N] {
                fn input<I: Input + ?Sized>(src: &mut I) -> Self {
                    let mut arr = std::mem::MaybeUninit::uninit();
                    unsafe {
                        let ptr = arr.as_mut_ptr() as *mut T;
                        for i in 0..$N {
                            ptr.add(i).write(src.input());
                        }
                        arr.assume_init()
                    }
                }
            })*
        };
    }
    array_impl! { 1 2 3 4 5 6 7 8 }
    #[macro_export]
    macro_rules! kdbg {
        ($($v:expr),*) => {
            if cfg!(debug_assertions) { dbg!($($v),*) } else { ($($v),*) }
        }
    }
}