#![allow(unused_imports)] use std::cmp::*; use std::collections::*; use std::io::Write; use std::ops::Bound::*; #[allow(unused_macros)] macro_rules! debug { ($($e:expr),*) => { #[cfg(debug_assertions)] $({ let (e, mut err) = (stringify!($e), std::io::stderr()); writeln!(err, "{} = {:?}", e, $e).unwrap() })* }; } fn main() { let mut r = [0; 3]; let mut m = [0; 3]; for i in 0..3 { let v = read_vec::(); r[i] = v[0]; m[i] = v[1]; } if let Some((x, y)) = crt(&r, &m) { println!("{}", x); } else { println!("-1"); } } fn read() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } fn read_vec() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } pub fn inv_gcd(a: i64, b: i64) -> (i64, i64) { let a = a.rem_euclid(b); if a == 0 { return (b, 0); } let mut s = b; let mut t = a; let mut m0 = 0; let mut m1 = 1; while t != 0 { let u = s / t; s -= t * u; m0 -= m1 * u; std::mem::swap(&mut s, &mut t); std::mem::swap(&mut m0, &mut m1); } if m0 < 0 { m0 += b / s; } (s, m0) } // return y (mod z) pub fn crt(r: &[i64], m: &[i64]) -> Option<(i64, i64)> { assert_eq!(r.len(), m.len()); // Contracts: 0 <= r0 < m0 let (mut r0, mut m0) = (0, 1); for (&(mut ri), &(mut mi)) in r.iter().zip(m.iter()) { assert!(1 < mi); ri = ri.rem_euclid(mi); if m0 < mi { std::mem::swap(&mut r0, &mut ri); std::mem::swap(&mut m0, &mut mi); } if m0 % mi == 0 { if r0 % mi != ri { return None; } continue; } let (g, im) = inv_gcd(m0, mi); let u1 = mi / g; // |ri - r0| < (m0 + mi) <= lcm(m0, mi) if (ri - r0) % g != 0 { return None; } let x = (ri - r0) / g % u1 * im % u1; r0 += x * m0; m0 *= u1; // -> lcm(m0, mi) if r0 < 0 { r0 += m0 }; } Some((r0, m0)) }