結果

問題 No.1287 えぬけー
コンテスト
ユーザー nebocco
提出日時 2021-02-16 20:35:08
言語 Rust
(1.83.0 + proconio)
結果
RE  
実行時間 -
コード長 6,879 bytes
コンパイル時間 13,224 ms
コンパイル使用メモリ 399,184 KB
実行使用メモリ 14,340 KB
最終ジャッジ日時 2024-09-13 10:15:24
合計ジャッジ時間 18,131 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other RE * 1 TLE * 1 -- * 3
権限があれば一括ダウンロードができます

ソースコード

diff # 

fn main() {
	let mut io = IO::new();
    input!{ from io,
		t: usize,
		query: [(i64, i64); t]
    }
	for &(x, k) in &query {
		io.println(solve(x, k));
	}
}

fn solve(x: i64, k: i64) -> i64 {
	let sigma = 5;
	const MOD: i64 = 1_000_000_007;
	let cx = baby_giant(sigma, x, MOD).unwrap();
	let k_inv = modinv(k, MOD-1);
	return modpow(sigma, k_inv * cx, MOD);
}

pub fn modinv(mut x: i64, modulo: i64) -> i64 {
    x = x.rem_euclid(modulo);
    extgcd(x, modulo).0.rem_euclid(modulo)
}

// return (x, y) s.t. a * x + b * y = gcd(a, b)
pub fn extgcd(a: i64, b: i64) -> (i64, i64) {
    let mut x1 = 1;
    let mut y1 = 0;
    let mut m = a;
    let mut x2 = 0;
    let mut y2 = 1;
    let mut n = b;
    while m % n != 0 {
        let q = m / n;
        x1 -= q * x2;
        y1 -= q * y2;
        m -= q * n;
        std::mem::swap(&mut x1, &mut x2);
        std::mem::swap(&mut y1, &mut y2);
        std::mem::swap(&mut m, &mut n);
    }
    (x2, y2)
}

pub fn modpow(x: i64, mut y: i64, modulo: i64) -> i64 {
    let mut ret = 1;
    let mut cur = x;
    while y > 0 {
        if y & 1 > 0 {
            ret = ret * cur % modulo;
        }
        cur = cur * cur % modulo;
        y >>= 1;
    }
    ret
}

use std::collections::HashMap;

pub fn baby_giant(x: i64, y: i64, modulo: i64) -> Option<i64> {
    if (y - 1) % modulo == 0 { return Some(0); }
    if y == 0 {
        let (mut lo, mut hi) = (0, modulo);
        while hi - lo > 1 {
            let mid = (hi + lo) / 2;
            if modpow(x, mid, modulo) == 0 {
                hi = mid;
            } else {
                lo = mid;
            }
        }
        return if modpow(x, hi, modulo) == 0 {
            Some(hi)
        } else {
            None
        };
    }
    let mut dic: HashMap<i64, i64> = HashMap::new();
    let sq = (modulo as f64).sqrt() as i64 + 1;
    let mut z = y;
    for i in 0..sq {
        // dic[y * x ^ i] = i
        dic.insert(z, i);
        z = z * x % modulo;
    }
    let r = modpow(x, sq, modulo); // r = x ^ (-sq)
    let mut c = 1;
    for i in 1..=sq {
        c = c * r % modulo;
        if let Some(v) = dic.get(&c) {
            let res = i * sq - v;
            return if modpow(x, res, modulo) == y {
                Some(res)
            } else {
                None
            };
        }
    }
    None
}

// ------------ io module start ------------
use std::io::{stdout, BufWriter, Read, StdoutLock, Write};

pub struct IO {
	iter: std::str::SplitAsciiWhitespace<'static>,
	buf: BufWriter<StdoutLock<'static>>,
}

impl IO {
	pub fn new() -> Self {
		let mut input = String::new();
		std::io::stdin().read_to_string(&mut input).unwrap();
		let input = Box::leak(input.into_boxed_str());
		let out = Box::new(stdout());
		IO {
			iter: input.split_ascii_whitespace(),
			buf: BufWriter::new(Box::leak(out).lock()),
		}
	}
	fn scan_str(&mut self) -> &'static str {
		self.iter.next().unwrap()
	}
	pub fn scan<T: Scan>(&mut self) -> <T as Scan>::Output {
		<T as Scan>::scan(self)
	}
	pub fn scan_vec<T: Scan>(&mut self, n: usize) -> Vec<<T as Scan>::Output> {
		(0..n).map(|_| self.scan::<T>()).collect()
	}
	pub fn print<T: Print>(&mut self, x: T) {
		<T as Print>::print(self, x);
	}
	pub fn println<T: Print>(&mut self, x: T) {
		self.print(x);
		self.print("\n");
	}
	pub fn iterln<T: Print, I: Iterator<Item = T>>(&mut self, mut iter: I, delim: &str) {
		if let Some(v) = iter.next() {
			self.print(v);
			for v in iter {
				self.print(delim);
				self.print(v);
			}
		}
		self.print("\n");
	}
	pub fn flush(&mut self) {
		self.buf.flush().unwrap();
	}
}

impl Default for IO {
	fn default() -> Self {
		Self::new()
	}
}

pub trait Scan {
	type Output;
	fn scan(io: &mut IO) -> Self::Output;
}

macro_rules! impl_scan {
	($($t:tt),*) => {
		$(
			impl Scan for $t {
				type Output = Self;
				fn scan(s: &mut IO) -> Self::Output {
					s.scan_str().parse().unwrap()
				}
			}
		)*
	};
}

impl_scan!(i16, i32, i64, isize, u16, u32, u64, usize, String);

pub enum Bytes {}
impl Scan for Bytes {
	type Output = &'static [u8];
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().as_bytes()
	}
}

pub enum Chars {}
impl Scan for Chars {
	type Output = Vec<char>;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().collect()
	}
}

pub enum Usize1 {}
impl Scan for Usize1 {
	type Output = usize;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan::<usize>().wrapping_sub(1)
	}
}

impl<T: Scan, U: Scan> Scan for (T, U) {
	type Output = (T::Output, U::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan> Scan for (T, U, V) {
	type Output = (T::Output, U::Output, V::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s))
	}
}

impl<T: Scan, U: Scan, V: Scan, W: Scan> Scan for (T, U, V, W) {
	type Output = (T::Output, U::Output, V::Output, W::Output);
	fn scan(s: &mut IO) -> Self::Output {
		(T::scan(s), U::scan(s), V::scan(s), W::scan(s))
	}
}

pub trait Print {
	fn print(w: &mut IO, x: Self);
}

macro_rules! impl_print_int {
	($($t:ty),*) => {
		$(
			impl Print for $t {
				fn print(w: &mut IO, x: Self) {
					w.buf.write_all(x.to_string().as_bytes()).unwrap();
				}
			}
		)*
	};
}

impl_print_int!(i16, i32, i64, isize, u16, u32, u64, usize);

impl Print for u8 {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(&[x]).unwrap();
	}
}

impl Print for &[u8] {
	fn print(w: &mut IO, x: Self) {
		w.buf.write_all(x).unwrap();
	}
}

impl Print for &str {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl Print for String {
	fn print(w: &mut IO, x: Self) {
		w.print(x.as_bytes());
	}
}

impl<T: Print, U: Print> Print for (T, U) {
	fn print(w: &mut IO, (x, y): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
	}
}

impl<T: Print, U: Print, V: Print> Print for (T, U, V) {
	fn print(w: &mut IO, (x, y, z): Self) {
		w.print(x);
		w.print(" ");
		w.print(y);
		w.print(" ");
		w.print(z);
	}
}

mod neboccoio_macro {
	#[macro_export]
	macro_rules! input {
		(@start $io:tt @read @rest) => {};

		(@start $io:tt @read @rest, $($rest: tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @rest mut $($rest:tt)*) => {
			input!(@start $io @read @mut [mut] @rest $($rest)*)
		};

		(@start $io:tt @read @rest $($rest:tt)*) => {
			input!(@start $io @read @mut [] @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:tt] $($rest:tt)*) => {
			let $($mut)* $var = $io.scan_vec::<$kind>($len);
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: $kind:tt $($rest:tt)*) => {
			let $($mut)* $var = $io.scan::<$kind>();
			input!(@start $io @read @rest $($rest)*)
		};

		(from $io:tt $($rest:tt)*) => {
			input!(@start $io @read @rest $($rest)*)
		};
	}
}

// ------------ io module end ------------
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