結果

問題 No.109 N! mod M
ユーザー nebocconebocco
提出日時 2021-03-11 19:24:37
言語 Rust
(1.77.0 + proconio)
結果
AC  
実行時間 97 ms / 5,000 ms
コード長 6,308 bytes
コンパイル時間 13,677 ms
コンパイル使用メモリ 379,756 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-13 07:09:10
合計ジャッジ時間 13,850 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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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
5,248 KB
testcase_01 AC 54 ms
5,248 KB
testcase_02 AC 65 ms
5,248 KB
testcase_03 AC 1 ms
5,248 KB
testcase_04 AC 3 ms
5,248 KB
testcase_05 AC 97 ms
5,248 KB
testcase_06 AC 4 ms
5,248 KB
testcase_07 AC 11 ms
5,248 KB
testcase_08 AC 1 ms
5,248 KB
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ソースコード

diff # 

fn main() {
	let mut io = IO::new();
    input!{ from io,
		t: usize,
		query: [(i64, i64); t]
    }
	for &(n, m) in &query {
		if n >= m {
			io.println(0);
		} else if m < 200_100 {
			let ans = (1..=n).fold(1, |sum, x| sum * x % m) % m;
			io.println(ans);
		} else {
			if is_prime(m) {
				let f = (n+1..m).fold(1, |sum, x| sum * x % m) % m;
				io.println((m - 1) * modinv(f, m) % m);
			} else {
				io.println(0);
			}
		}
	}
}

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 is_prime(x: i64) -> bool {
    (2..=sqrt_floor(x)).all(|i| x % i != 0)
}

pub fn sqrt_floor(x: i64) -> i64 {
    let c = (64 - x.leading_zeros() + 1) / 2;
    let mut v = if c < 32 {
        1 << c
    } else {
        3_037_000_499
    };
    while v * v > x {
        v = (v + x / v) / 2;
    }
    v
}


// ------------ 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, f32, f64);

impl Scan for char {
	type Output = char;
	fn scan(s: &mut IO) -> Self::Output {
		s.scan_str().chars().next().unwrap()
	}
}

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, f32, f64);

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; $len1:expr]; $len2:expr] $($rest:tt)*) => {
			let $($mut)* $var = (0..$len2).map(|_| $io.scan_vec::<$kind>($len1)).collect::<Vec<Vec<$kind>>>();
			input!(@start $io @read @rest $($rest)*)
		};

		(@start $io:tt @read @mut [$($mut:tt)?] @rest $var:tt: [$kind:tt; $len:expr] $($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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