#![allow(dead_code)] #![allow(unused_imports)] #![allow(unused_macros)] 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 = MOD9; const UMOD: usize = MOD as usize; const M_PI: f64 = 3.14159265358979323846; use cmp::Ordering::*; use std::collections::*; use std::io::stdin; use std::io::stdout; use std::io::Write; macro_rules! p { ($x:expr) => { println!("{}", $x); }; } macro_rules! vp { ($x:expr) => { println!( "{}", $x.iter() .map(|x| x.to_string()) .collect::>() .join(" ") ); }; } macro_rules! d { ($x:expr) => { eprintln!("{:?}", $x); }; } macro_rules! yn { ($val:expr) => { if $val { println!("Yes"); } else { println!("No"); } }; } macro_rules! map{ ($($key:expr => $val:expr),*) => { { let mut map = ::std::collections::BTreeMap::new(); $( map.insert($key, $val); )* map } }; } macro_rules! set{ ($($key:expr),*) => { { let mut set = ::std::collections::BTreeSet::new(); $( set.insert($key); )* set } }; } #[allow(dead_code)] fn read() -> 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() -> Vec { read::() .split_whitespace() .map(|e| e.parse().ok().unwrap()) .collect() } #[allow(dead_code)] fn read_mat(n: usize) -> Vec> { (0..n).map(|_| read_vec()).collect() } #[allow(dead_code)] fn readii() -> (i64, i64) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } #[allow(dead_code)] fn readiii() -> (i64, i64, i64) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2]) } #[allow(dead_code)] fn readuu() -> (usize, usize) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } #[allow(dead_code)] fn readff() -> (f64, f64) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } fn readcc() -> (char, char) { let mut vec: Vec = read_vec(); (vec[0], vec[1]) } fn readuuu() -> (usize, usize, usize) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2]) } #[allow(dead_code)] fn readiiii() -> (i64, i64, i64, i64) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2], vec[3]) } #[allow(dead_code)] fn readuuuu() -> (usize, usize, usize, usize) { let mut vec: Vec = read_vec(); (vec[0], vec[1], vec[2], vec[3]) } use proconio::input; use std::cmp::{max, min}; fn gcd(a: i64, b: i64) -> i64 { if b == 0 { a.abs() } else { gcd(b, a % b) } } fn extended_gcd_fn(a: i64, b: i64) -> (i64, i64, i64) { if b == 0 { (a.abs(), a.signum(), 0) } else { let (g, x1, y1) = extended_gcd_fn(b, a % b); let x = y1; let y = x1 - (a / b) * y1; (g, x, y) } } fn ceil_div(a: i64, b: i64) -> i64 { if b < 0 { return ceil_div(-a, -b); } if a >= 0 { (a + b - 1) / b } else { a / b } } fn floor_div(a: i64, b: i64) -> i64 { if b < 0 { return floor_div(-a, -b); } if a >= 0 { a / b } else { (a - b + 1) / b } } fn main() { input! { T: usize, test_cases: [(i64, i64, i64); T], } for &(D, x, y) in &test_cases { let S: i64; if x == 0 && y != 0 { if y <= D { S = y * D; } else { S = 0; } } else if y == 0 && x != 0 { if x <= D { S = x * D; } else { S = 0; } } else if x != 0 && y != 0 { let C = x * x + y * y; let g = gcd(x, y); let x_prime = x / g; let y_prime = y / g; let C_prime = C / g; let (gcd_val, a, b) = extended_gcd_fn(x_prime, y_prime); let mut u0 = a * C_prime; let mut v0 = b * C_prime; let k1 = ceil_div(-u0, y_prime); let k2 = ceil_div(v0 - D, x_prime); let k_min = max(k1, k2); let k3 = floor_div((D - u0), y_prime); let k4 = floor_div(v0, x_prime); let k_max = min(k3, k4); if k_min > k_max { S = 0; } else { let v1 = v0 - k_min * x_prime; let v2 = v0 - k_max * x_prime; let dist1 = (v1 - y).abs(); let dist2 = (v2 - y).abs(); let max_dist = max(dist1, dist2); S = (C * max_dist) / x; } } else { S = 0; } println!("{}", S); } }