// 桁数固定してみる // |X| = x として // X 10^(k+x) + A * 10^x + X // がMの倍数かつA<10^k になるかという問題 // use std::io::Write; use std::collections::*; type Map = BTreeMap; type Set = BTreeSet; type Deque = VecDeque; fn run() { input! { t: usize, ask: [(bytes, i64); t], } let out = std::io::stdout(); let mut out = std::io::BufWriter::new(out.lock()); for (x, m) in ask { if let Some(y) = solve(x, m) { writeln!(out, "{}", y.iter().map(|c| *c as char).collect::()).ok(); } else { writeln!(out, "-1").ok(); } } } fn main() { run(); } fn solve(x: Vec, m: i64) -> Option> { let v = x.iter().fold(0, |s, a| s * 10 + (*a - b'0')) as i64; let l = x.len(); for i in l..=18 { if i < 2 * l { let mut ans = vec![b'0' - 1; i]; for j in 0..l { ans[j] = x[j]; } for j in 0..l { if ans[i - l + j] != b'0' - 1 && ans[i - l + j] != x[j] { break; } ans[i - l + j] = x[j]; } if ans.iter().all(|a| *a >= b'0') && ans.iter().fold(0, |s, a| s * 10 + (*a - b'0') as i64) % m == 0 { return Some(ans); } continue; } let f = i - 2 * l; let rhs = (-v * (1 + 10i64.pow(i as u32 - l as u32))).rem_euclid(m); // 10^l * A = rhs (mod M) let p = 10i64.pow(l as u32); let g = gcd(p, m); if rhs % g != 0 { continue; } let p = p / g; let rhs = rhs / g; let m = m / g; let (a, b) = calc(p, m); let mut r = (rhs * a).rem_euclid(m); if r >= 10i64.pow(f as u32) { continue; } let mut ans = vec![b'0'; i]; for j in 0..l { ans[j] = x[j]; ans[i - l + j] = x[j]; } for a in ans[l..(i - l)].iter_mut().rev() { *a = b'0' + (r % 10) as u8; r /= 10; } return Some(ans) } None } fn gcd(a: i64, b: i64) -> i64 { if b == 0 { a.abs() } else { gcd(b, a.rem_euclid(b.abs())) } } // return (a, b) // ax + by = gcd(x, y) fn calc(x: i64, y: i64) -> (i64, i64) { if y == 0 { return (x.signum(), 0); } let q = x.div_euclid(y); let r = x.rem_euclid(y); let p = calc(y, r); (p.1, p.0 - q * p.1) } // ---------- 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 ----------