//https://github.com/manta1130/Competitive_Programming_Template_Rust #[macro_use] mod input { use std; use std::io; const SPLIT_DELIMITER: char = ' '; #[macro_export] #[allow(unused_macros)] macro_rules! input { ( $($x:expr ),*) => { { let temp_str = input_line_str(); let mut split_result_iter = temp_str.split_whitespace(); $( let buf_split_result = split_result_iter.next(); let buf_split_result = buf_split_result.unwrap(); ($x) = buf_split_result.parse().unwrap(); )* } }; } #[allow(dead_code)] pub fn input_line_str() -> String { let mut s = String::new(); io::stdin().read_line(&mut s).unwrap(); s.trim().to_string() } #[allow(dead_code)] pub fn p(t: T) where T: std::fmt::Display, { println!("{}", t); } #[allow(dead_code)] pub fn input_vector2d(line: usize) -> Vec> where T: std::str::FromStr, { let mut v: Vec> = Vec::new(); for _ in 0..line { let vec_line = input_vector(); v.push(vec_line); } v } #[allow(dead_code)] pub fn input_vector() -> Vec where T: std::str::FromStr, { let mut v: Vec = Vec::new(); let s = input_line_str(); let split_result = s.split(SPLIT_DELIMITER); for z in split_result { let buf = match z.parse() { Ok(r) => r, Err(_) => panic!("Parse Error"), }; v.push(buf); } v } #[allow(dead_code)] pub fn input_vector_row(n: usize) -> Vec where T: std::str::FromStr, { let mut v = Vec::with_capacity(n); for _ in 0..n { let buf = match input_line_str().parse() { Ok(r) => r, Err(_) => panic!("Parse Error"), }; v.push(buf); } v } pub trait ToCharVec { fn to_charvec(&self) -> Vec; } impl ToCharVec for String { fn to_charvec(&self) -> Vec { self.to_string().chars().collect::>() } } } //https://github.com/rust-lang-ja/ac-library-rs use input::*; use std::mem::swap; fn inv_gcd(a: i64, b: i64) -> (i64, i64) { let a = safe_mod(a, b); if a == 0 { return (b, 0); } // Contracts: // [1] s - m0 * a = 0 (mod b) // [2] t - m1 * a = 0 (mod b) // [3] s * |m1| + t * |m0| <= b 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; // |m1 * u| <= |m1| * s <= b // [3]: // (s - t * u) * |m1| + t * |m0 - m1 * u| // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u) // = s * |m1| + t * |m0| <= b swap(&mut s, &mut t); swap(&mut m0, &mut m1); } // by [3]: |m0| <= b/g // by g != b: |m0| < b/g if m0 < 0 { m0 += b / s; } (s, m0) } fn safe_mod(mut x: i64, m: i64) -> i64 { x %= m; if x < 0 { x += m; } x } fn crt(r: &Vec, m: &Vec) -> (i64, i64) { assert!(r.len() == m.len()); let n = r.len(); // Contracts: 0 <= r0 < m0 let (mut r0, mut m0) = (0, 1); for (ri, mi) in r.iter().zip(m.iter()) { assert!(1 < *mi); let mut r1 = safe_mod(*ri, *mi); let mut m1 = *mi; if m0 < m1 { swap(&mut r0, &mut r1); swap(&mut m0, &mut m1); } if m0 % m1 == 0 { if r0 % m1 != r1 { return (0, 0); } continue; } // assume: m0 > m1, lcm(m0, m1) >= 2 * max(m0, m1) // (r0, m0), (r1, m1) -> (r2, m2 = lcm(m0, m1)); // r2 % m0 = r0 // r2 % m1 = r1 // -> (r0 + x*m0) % m1 = r1 // -> x*u0*g % (u1*g) = (r1 - r0) (u0*g = m0, u1*g = m1) // -> x = (r1 - r0) / g * inv(u0) (mod u1) // im = inv(u0) (mod u1) (0 <= im < u1) let (g, im) = inv_gcd(m0, m1); let u1 = m1 / g; // |r1 - r0| < (m0 + m1) <= lcm(m0, m1) if (r1 - r0) % g != 0 { return (0, 0); } // u1 * u1 <= m1 * m1 / g / g <= m0 * m1 / g = lcm(m0, m1) let x = (r1 - r0) / g % u1 * im % u1; // |r0| + |m0 * x| // < m0 + m0 * (u1 - 1) // = m0 + m0 * m1 / g - m0 // = lcm(m0, m1) r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if r0 < 0 { r0 += m0 }; } (r0, m0) } fn main() { let n: usize; input!(n); let mut x = vec![]; let mut y = vec![]; for _ in 0..n { let (q, w): (i64, i64); input!(q, w); x.push(q); y.push(w); } let ans = crt(&x, &y); if ans.0 == 0 && ans.1 == 0 { println!("-1"); } else { println!("{}", ans.0 % 1_000_000_007); } }