#[allow(unused_imports)] use std::cmp::*; #[allow(unused_imports)] use std::collections::*; use std::io::{Write, BufWriter}; // https://qiita.com/tanakh/items/0ba42c7ca36cd29d0ac8 macro_rules! input { ($($r:tt)*) => { let stdin = std::io::stdin(); let mut bytes = std::io::Read::bytes(std::io::BufReader::new(stdin.lock())); let mut next = move || -> String{ bytes .by_ref() .map(|r|r.unwrap() as char) .skip_while(|c|c.is_whitespace()) .take_while(|c|!c.is_whitespace()) .collect() }; input_inner!{next, $($r)*} }; } macro_rules! input_inner { ($next:expr) => {}; ($next:expr, ) => {}; ($next:expr, $var:ident : $t:tt $($r:tt)*) => { let $var = read_value!($next, $t); input_inner!{$next $($r)*} }; } macro_rules! read_value { ($next:expr, ( $($t:tt),* )) => { ( $(read_value!($next, $t)),* ) }; ($next:expr, [ $t:tt ; $len:expr ]) => { (0..$len).map(|_| read_value!($next, $t)).collect::>() }; ($next:expr, chars) => { read_value!($next, String).chars().collect::>() }; ($next:expr, usize1) => { read_value!($next, usize) - 1 }; ($next:expr, [ $t:tt ]) => {{ let len = read_value!($next, usize); (0..len).map(|_| read_value!($next, $t)).collect::>() }}; ($next:expr, $t:ty) => { $next().parse::<$t>().expect("Parse error") }; } #[allow(unused)] macro_rules! debug { ($($format:tt)*) => (write!(std::io::stderr(), $($format)*).unwrap()); } #[allow(unused)] macro_rules! debugln { ($($format:tt)*) => (writeln!(std::io::stderr(), $($format)*).unwrap()); } fn powmod(x: i64, mut e: i64, m: i64) -> i64 { let mut sum = 1; let mut cur = x % m; while e > 0 { if e % 2 != 0 { sum = sum * cur % m; } cur = cur * cur % m; e /= 2; } sum } fn extgcd(x: i64, y: i64) -> (i64, i64, i64) { if y == 0 { return (x, 1, 0); } let r = x % y; let q = x / y; let (g, a, b) = extgcd(y, r); (g, b, a - b * q) } // Baby-step giant-step. https://codeforces.com/contest/1106/submission/49502575 // Find x s.t. x^exp = m fn modroot(m: i64, exp: i64, p: i64) -> Option { // prime factors of p - 1 let mut rel = vec![]; { let mut v = p - 1; let mut q = 2; while v > 1 && v >= q * q { if v % q == 0 { rel.push(q); while v % q == 0 { v /= q; } } q += 1; } if v > 1 { rel.push(v); } } let mut gen = 2; loop { let ok = rel.iter().all(|q| powmod(gen, (p - 1) / q, p) != 1); if ok { break; } gen += 1; } const SQRT: i64 = 40000; let mut cur = 1; let prog = powmod(gen, SQRT, p); let mut tbl = HashMap::new(); for i in 0..SQRT { tbl.insert(cur, SQRT * i); cur = cur * prog % p; } let discrete_log = |x: i64| { for i in 0..SQRT { let key = x * powmod(gen, i, p) % p; if let Some(&y) = tbl.get(&key) { return (y - i + p - 1) % (p - 1); } } unreachable!(); }; let logm = discrete_log(m); let (g, inv, _) = extgcd(exp, p - 1); if logm % g != 0 { return None; } let inv = (inv + p - 1) % (p - 1); let ans = (logm / g * inv) % (p - 1); Some(powmod(gen, ans, p)) } fn solve() { let out = std::io::stdout(); let mut out = BufWriter::new(out.lock()); macro_rules! puts { ($($format:tt)*) => (let _ = write!(out,$($format)*);); } input! { pka: [(i64, i64, i64)], } for (p, k, a) in pka { let ans = modroot(a, k, p); puts!("{}\n", ans.unwrap_or(-1)); } } fn main() { // In order to avoid potential stack overflow, spawn a new thread. let stack_size = 104_857_600; // 100 MB let thd = std::thread::Builder::new().stack_size(stack_size); thd.spawn(|| solve()).unwrap().join().unwrap(); }