from random import randint from collections import Counter class Prime(): def __init__(self, m=10**6): self.m = m self.isprime = [True] * (m + 1) self.minfac = [-1] * (m + 1) self.mobius = [1] * (m + 1) self.isprime[0] = self.isprime[1] = False self.minfac[1] = 1 for p in range(2, m + 1): if not self.isprime[p]: continue self.minfac[p] = p self.mobius[p] = -1 for q in range(2 * p, m + 1, p): self.isprime[q] = False if self.minfac[q] == -1: self.minfac[q] = p if (q // p) % p: self.mobius[q] *= -1 else: self.mobius[q] = 0 def gcd(self, x, y): while y: x, y = y, x % y return x def lcm(self, x, y): return x // self.gcd(x, y) * y def is_prime(self, n): if n <= self.m: return self.isprime[n] if not n & 1: return False return self.miller_rabin(n) def miller_rabin(self, n): if n <= 4294967295: p = [2, 7, 61] elif n <= 281474976710655: p = [2, 3, 5, 7, 11, 13, 17] elif n <= 18446744073709551615: p = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29] else: p = [randint(1, n - 1) for _ in range(20)] d = n - 1 d = d // (d & -d) for a in p: t = d y = pow(a, t, n) if y == 1: continue while y != n - 1: y = (y * y) % n if y == 1 or t == n - 1: return False t <<= 1 return True def factorize(self, n): if n <= self.m: return self.factorize_fast(n) if self.is_prime(n): return [n] res = [] stack = [n] while stack: tmp = stack.pop() if tmp <= self.m: res.extend(self.factorize_fast(tmp)) continue p = self.pollard_rho(tmp) q = tmp // p pri_p = self.is_prime(p) pri_q = self.is_prime(q) if pri_p and pri_q: res.append(p) res.append(q) elif pri_p: res.append(p) while not q % p: res.append(p) q //= p if self.is_prime(q): res.append(q) else: stack.append(q) elif pri_q: res.append(q) while not p % q: res.append(q) p //= q if self.is_prime(p): res.append(p) else: stack.append(p) else: stack.append(p) stack.append(q) return sorted(res) def factorize_fast(self, n): res = [] while n > 1: p = self.minfac[n] while self.minfac[n] == p: n //= p res.append(p) return sorted(res) def factorize_naive(self, n): res = [] x, y = n, 2 while y * y <= x: while not x % y: res.append(y) x //= y y += 1 if x > 1: res.append(x) return sorted(res) def pollard_rho(self, n): m = int(n**0.125) + 1 s = randint(1, 1000) while True: y, r, q = 2, 1, 1 d = 1 while d == 1: x = y for _ in range(r): y = (y * y + s) % n for k in range(0, r, m): ys = y for i in range(min(m, r - k)): y = (y * y + s) % n q = q * abs(x - y) % n d = self.gcd(n, q) if d != 1: break r <<= 1 if d == n: while d == 1: ys = (ys * ys + s) % n d = self.gcd(n, abs(x - ys)) if d != n: break s += 1 return d def divisors(self, n): if n <= self.m: return self.divisors_fast(n) if self.is_prime(n): return [1, n] return self.divisors_naive(n) def divisors_fast(self, n): res = [1] f = Counter(self.factorize_fast(n)) for p, d in f.items(): s = len(res) for i in range(s): v = 1 for j in range(d): v *= p res.append(res[i] * v) return sorted(res) def divisors_naive(self, n): res = [] x, y = n, 1 while y * y < x: if not x % y: res.append(y) res.append(x // y) y += 1 if y * y == x: res.append(y) return sorted(res) def zeta_transform(self, arr): n = len(arr) assert n <= self.m res = arr.copy() for p in range(2, n): if not self.isprime[p]: continue for k in range(1, (n - 1) // p + 1)[::-1]: res[k] += res[k * p] return res def mobius_transform(self, arr): n = len(arr) assert n <= self.m res = arr.copy() for p in range(2, n): if not self.isprime[p]: continue for k in range(p, n, p): res[k // p] -= res[k] return res def convolution_gcd(self, f, g): assert len(f) == len(g) F = self.zeta_transform(f) G = self.zeta_transform(g) H = [u * v for u, v in zip(F, G)] h = self.mobius_transform(H) return h P = Prime(100000) from math import gcd, sqrt def primitive_root(m): if m == 2: return 1 divs = set(P.factorize(m - 1)) g = 2 while True: for d in divs: if pow(g, (m - 1) // d, m) == 1: break else: return g g += 1 def discrete_logarithm(x, y, m): if m == 1: return 0 if y == 1: return 0 if x == y == 0: return 1 sq = int(sqrt(m)) + 1 powx = {} p = 1 for i in range(sq + 1): if p % m == y: return i powx[p * y % m] = i p *= x p %= m z = pow(x, sq, m) g = z for i in range(1, sq + 1): if g in powx: res = i * sq - powx[g] if pow(x, res, m) == y: return res g *= z g %= m return -1 def inv_gcd(a, b): a %= b if a == 0: return b, 0 s, t, m0, m1 = b, a, 0, 1 while t: u = s // t s -= t * u m0 -= m1 * u s, t = t, s m0, m1 = m1, m0 if m0 < 0: m0 += b // s return s, m0 def inv_mod(x, m): g, im = inv_gcd(x, m) return im def kth_root(k, y, p): if k == 0: if y == 1: return 0 else: return -1 if y == 0: return 0 g = gcd(k, p - 1) m = (p - 1) // g if pow(a, m, p) != 1: return -1 r = primitive_root(p) l = discrete_logarithm(r, y, p) if l % g: return -1 res = pow(r, l // g * inv_mod(k // g, m) % m, p) return res T = int(input()) for _ in range(T): p, k, a = map(int, input().split()) print(kth_root(k, a, p))