#include #include #include using namespace std; int binpow(int a, int b, int mod) { int ans = 1; while (b > 0) { if (b & 1) ans = 1LL * ans * a % mod; a = 1LL * a * a % mod; b >>= 1; } return ans; } int find_primitive_root(int p) { // Time complexity: O(p^(1/4+eps)) int x = p - 1; vector checks; for (int i = 2; i * i <= x; ++i) { if (x % i == 0) { while (x % i == 0) x /= i; checks.push_back((p - 1) / i); } } if (x > 1) { checks.push_back((p - 1) / x); } for (int i = 2; i < p; ++i) { bool ok = true; for (int j : checks) { if (binpow(i, j, p) == 1) { ok = false; break; } } if (ok) return i; } return -1; } int main() { int Q; cin >> Q; while (Q--) { int P, K, A; cin >> P >> K >> A; int g = find_primitive_root(P); int b = binpow(g, K, P); int bucket = 0; while (bucket * bucket < P) { ++bucket; } int mul = 1; vector val(bucket), perm(bucket); for (int i = 0; i < bucket; ++i) { val[i] = mul; perm[i] = i; mul = 1LL * mul * b % P; } sort(perm.begin(), perm.end(), [&](int i, int j) { return val[i] < val[j]; }); int pmul = 1, ans = -1; mul = binpow(mul, P - 2, P); for (int i = 0; i < bucket; ++i) { int target = 1LL * A * pmul % P; int l = 0, r = bucket; while (r - l > 1) { int m = (l + r) >> 1; if (val[perm[m]] <= target) l = m; else r = m; } if (val[perm[l]] == target) { ans = binpow(g, i * bucket + perm[l], P); break; } pmul = 1LL * pmul * mul % P; } cout << ans << '\n'; } return 0; }