use std::io::Read; fn get_word() -> String { let stdin = std::io::stdin(); let mut stdin=stdin.lock(); let mut u8b: [u8; 1] = [0]; loop { let mut buf: Vec = Vec::with_capacity(16); loop { let res = stdin.read(&mut u8b); if res.unwrap_or(0) == 0 || u8b[0] <= b' ' { break; } else { buf.push(u8b[0]); } } if buf.len() >= 1 { let ret = String::from_utf8(buf).unwrap(); return ret; } } } #[allow(dead_code)] fn get() -> T { get_word().parse().ok().unwrap() } fn nth(a: i64, n: i64) -> i64 { if a <= 1 { return a; } let mut pass = 0; let mut fail = std::cmp::min(a, 1 << 32) + 1; while fail - pass > 1 { let mid = (fail + pass) / 2; let mut tmp = 1i64; for _ in 0..n { tmp = tmp.saturating_mul(mid); } if tmp <= a { pass = mid; } else { fail = mid; } } pass } // Solves y = x(a-x) (x>=0) fn calc(a: i64, y: i64) -> Option { if 4 * y > a * a { return None; } let sd = nth(a * a - 4 * y, 2); if sd * sd != a * a - 4 * y { return None; } Some((a - sd) / 2) } fn solve(s: i64, t: i64) -> Vec<(i64, i64, i64)> { if t % 2 != 0 || 18 * s >= t * t { return vec![]; } let t = t / 2; if s * s % t != 0 { return vec![]; } let q = s * s / t; // q = (t-a)(t-b)(a+b-t) let mut divs = vec![]; let mut d = 1; while d * d <= q { if q % d == 0 { divs.push(d); if q != d * d { divs.push(q / d); } } d += 1; } let mut ans = vec![]; for d in divs { if d >= t { continue; } let a = t - d; if let Some(x) = calc(a, q / d) { let b = t - x; if b <= 0 { continue; } let mut v = [a, b, 2 * t - a - b]; v.sort_unstable(); if v[2] <= 1_000_000_000 { ans.push((v[0], v[1], v[2])); } } } ans.sort_unstable(); ans.dedup(); ans } fn main() { let t: usize = get(); for _ in 0..t { let s: i64 = get(); let t: i64 = get(); let v = solve(s, t); println!("{}", v.len()); for (a, b, c) in v { println!("{} {} {}", a, b, c); } } }