// Q(N+M)=PNM // P^2NM - PQ(N+M) = 0 // (PN - Q)(PM - Q) - Q^2 = 0 fn run() { input!(p: u64, q: u64); let mut f = vec![]; let mut m = q; for p in 2.. { if p * p > m { break; } if m % p == 0 { f.push(p); while m % p == 0 { m /= p; } } } if m > 1 { f.push(m); } let mut m = q * q; let mut d = vec![1]; for &p in f.iter() { let len = d.len(); while m % p == 0 { for i in (d.len() - len)..d.len() { let v = d[i] * p; d.push(v); } m /= p; } } let mut ans = vec![]; for &d in d.iter() { if (d + q) % p == 0 && (q * q / d + q) % p == 0 { ans.push(((d + q) / p, (q * q / d + q) / p)); } } ans.sort(); ans.dedup(); println!("{}", ans.len()); for a in ans { println!("{} {}", a.0, a.1); } } fn main() { run(); } // ---------- begin input macro ---------- // reference: https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 #[macro_export] macro_rules! input { (source = $s:expr, $($r:tt)*) => { let mut iter = $s.split_whitespace(); input_inner!{iter, $($r)*} }; ($($r:tt)*) => { let s = { use std::io::Read; let mut s = String::new(); std::io::stdin().read_to_string(&mut s).unwrap(); s }; let mut iter = s.split_whitespace(); input_inner!{iter, $($r)*} }; } #[macro_export] macro_rules! input_inner { ($iter:expr) => {}; ($iter:expr, ) => {}; ($iter:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($iter, $t); input_inner!{$iter $($r)*} }; } #[macro_export] macro_rules! read_value { ($iter:expr, ( $($t:tt),* )) => { ( $(read_value!($iter, $t)),* ) }; ($iter:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($iter, $t)).collect::>() }; ($iter:expr, chars) => { read_value!($iter, String).chars().collect::>() }; ($iter:expr, bytes) => { read_value!($iter, String).bytes().collect::>() }; ($iter:expr, usize1) => { read_value!($iter, usize) - 1 }; ($iter:expr, $t:ty) => { $iter.next().unwrap().parse::<$t>().expect("Parse error") }; } // ---------- end input macro ----------