// -*- coding:utf-8-unix -*- // #![feature(map_first_last)] #![allow(dead_code)] #![allow(unused_imports)] #![allow(unused_macros)] // use core::num; use std::cmp::*; use std::fmt::*; use std::hash::*; use std::io::BufRead; use std::iter::FromIterator; use std::*; use std::{cmp, collections, fmt, io, iter, ops, str}; const INF: i64 = 1223372036854775807; const UINF: usize = INF as usize; const LINF: i64 = 2147483647; const INF128: i128 = 1223372036854775807000000000000; const MOD1: i64 = 1000000007; const MOD9: i64 = 998244353; const MOD: i64 = 1000000000; // const MOD: i64 = MOD2; const UMOD: usize = MOD as usize; const M_PI: f64 = 3.14159265358979323846; // use proconio::input; // const MOD: i64 = INF; use cmp::Ordering::*; use std::collections::*; use std::io::stdin; use std::io::stdout; use std::io::Write; macro_rules! p { ($x:expr) => { //if expr println!("{}", $x); }; } macro_rules! vp { // vector print separate with space ($x:expr) => { println!( "{}", $x.iter() .map(|x| x.to_string()) .collect::<Vec<_>>() .join(" ") ); }; } macro_rules! d { ($x:expr) => { eprintln!("{:?}", $x); }; } macro_rules! yn { ($val:expr) => { if $val { println!("Yes"); } else { println!("No"); } }; } macro_rules! map{ // declear btreemap ($($key:expr => $val:expr),*) => { { let mut map = ::std::collections::BTreeMap::new(); $( map.insert($key, $val); )* map } }; } macro_rules! set{ // declear btreemap ($($key:expr),*) => { { let mut set = ::std::collections::BTreeSet::new(); $( set.insert($key); )* set } }; } //input output #[allow(dead_code)] fn read<T: std::str::FromStr>() -> T { let mut s = String::new(); std::io::stdin().read_line(&mut s).ok(); s.trim().parse().ok().unwrap() } #[allow(dead_code)] fn read_vec<T: std::str::FromStr>() -> Vec<T> { read::<String>() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } #[allow(dead_code)] fn read_mat<T: std::str::FromStr>(n: usize) -> Vec<Vec<T>> { (0..n).map(|_| read_vec()).collect() } #[allow(dead_code)] fn readii() -> (i64, i64) { let mut vec: Vec<i64> = read_vec(); (vec[0], vec[1]) } #[allow(dead_code)] fn readiii() -> (i64, i64, i64) { let mut vec: Vec<i64> = read_vec(); (vec[0], vec[1], vec[2]) } #[allow(dead_code)] fn readuu() -> (usize, usize) { let mut vec: Vec<usize> = read_vec(); (vec[0], vec[1]) } #[allow(dead_code)] fn readff() -> (f64, f64) { let mut vec: Vec<f64> = read_vec(); (vec[0], vec[1]) } fn readcc() -> (char, char) { let mut vec: Vec<char> = read_vec(); (vec[0], vec[1]) } fn readuuu() -> (usize, usize, usize) { let mut vec: Vec<usize> = read_vec(); (vec[0], vec[1], vec[2]) } #[allow(dead_code)] fn readiiii() -> (i64, i64, i64, i64) { let mut vec: Vec<i64> = read_vec(); (vec[0], vec[1], vec[2], vec[3]) } #[allow(dead_code)] fn readuuuu() -> (usize, usize, usize, usize) { let mut vec: Vec<usize> = read_vec(); (vec[0], vec[1], vec[2], vec[3]) } fn extended_gcd(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a, 1, 0) } else { let (g, x1, y1) = extended_gcd(b, a % b); (g, y1, x1 - (a / b) * y1) } } fn mod_inverse(a: i64, m: i64) -> Option<i64> { let (g, x, _) = extended_gcd(a, m); if g != 1 { None } else { Some((x % m + m) % m) } } // use from_str use std::str::FromStr; // use gcd fn gcd(a: i64, b: i64) -> i64 { if b == 0 { a } else { gcd(b, a % b) } } fn solve() { let stdin = io::stdin(); let mut input = stdin.lock().lines(); let t: usize = input.next().unwrap().unwrap().trim().parse().unwrap(); let mut results = Vec::new(); for _ in 0..t { if let Some(line) = input.next() { let values: Vec<i64> = line .unwrap() .split_whitespace() .map(|s| i64::from_str(s).unwrap()) .collect(); let n = values[0]; let m = values[1]; let r = (MOD - (m % MOD)) % MOD; let g = gcd(n, MOD); if r % g != 0 { results.push("-1".to_string()); continue; } if r == 0 { results.push((MOD / g).to_string()); } else { let np = n / g; let rp = r / g; let mp = MOD / g; let inv = mod_inverse(np, mp).unwrap(); let mut k = (rp * inv) % mp; if k == 0 { k = mp; } results.push(k.to_string()); } } } println!("{}", results.join("\n")); } fn main() { solve(); }