pub fn read() -> T { use std::io::Read; std::io::stdin() .lock() .by_ref() .bytes() .map(|c| c.unwrap() as char) .skip_while(|c| c.is_whitespace()) .take_while(|c| !c.is_whitespace()) .collect::() .parse::() .ok() .unwrap() } pub fn extgcd(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { return if a < 0 { (-a, -1, 0) } else { (a, 1, 0) }; } let (g, s, t) = extgcd(b, a % b); (g, t, s - a / b * t) } pub fn mod_gcd_inv(modulus: usize, n: usize) -> (usize, usize) { let m = modulus as i64; let (g, mut x, _) = extgcd(n as i64 % m, m); let u = m / g; assert!(u > 0); if x < 0 { x += u; } assert!(0 <= x && x <= u && 1 <= g); (g as usize, x as usize) } pub fn safe_crt( mut m0: usize, mut r0: usize, mut m1: usize, mut r1: usize, ) -> Option<(usize, usize)> { use std::mem::swap; assert!(0 < m0 && 0 < m1); r0 %= m0; r1 %= m1; if m0 < m1 { // necessarily to avoid overflow swap(&mut r0, &mut r1); swap(&mut m0, &mut m1); } if m0 % m1 == 0 { return if r0 % m1 == r1 { Some((m0, r0)) } else { None }; } let (g, inv_u0) = mod_gcd_inv(m1, m0 % m1); // let rd = r1.abs_diff(r0); // to avoid overflow in case r1 < r0. v1.60 <= let rd = if r1 < r0 { r0 - r1 } else { r1 - r0 }; if rd % g != 0 { return None; } let u1 = m1 / g; let mut x = rd / g * inv_u0 % u1; // x <= m1^2. so if m0 < m1, it should be swapped at first. if r1 < r0 { x = u1 - x; } let mut r = r0 + x * m0; let lcm = m0 * u1; if r >= lcm { r -= lcm; } debug_assert!(r1.max(r0) <= r && r < lcm); Some((lcm, r)) } pub fn crt_prod(mr: &[(usize, usize)]) -> Option<(usize, usize)> { let (mut m0, mut r0) = (1, 0); for &(m1, r1) in mr.iter() { let (lcm, ans) = safe_crt(m0, r0, m1, r1)?; m0 = lcm; r0 = ans; assert!(r0 < m0); } Some((m0, r0)) } pub fn main() { use std::io::Write; let out = std::io::stdout(); let writer = &mut std::io::BufWriter::new(out.lock()); let mr: Vec<_> = (0..3) .map(|_| { let r: usize = read(); let m: usize = read(); (m, r) }) .collect(); if let Some((m, mut r)) = crt_prod(&mr) { if r == 0 { r += m; } writeln!(writer, "{}", r).unwrap(); } else { writeln!(writer, "{}", -1).unwrap(); } }