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#include <cstring>
#include <cstdlib>
#include <cassert>
#include <cctype>
#include <cmath>
#include <algorithm>
#include <functional>
#include <utility>
#include <vector>
#include <map>
#include <tr1/unordered_map>
typedef long long ll;
ll (ll a, ll b) {
if(!b) {
return a;
} else {
return gcd(b, a % b);
}
}
void exgcd(ll a, ll b, ll &d, ll &x, ll &y) {
if(!b) {
d = a; x = 1; y = 0;
} else {
ll nx, ny; exgcd(b, a % b, d, nx, ny);
x = ny; y = nx - ny * (a / b);
}
}
ll inv(ll v, ll p) {
ll d, x, y; exgcd(v, p, d, x, y);
return (x + p) % p;
}
ll pow_mod(ll a, ll b, ll p) {
ll ans = 1, res = a;
while(b) {
if(1LL & b) ans = ans * res % p;
res = res * res % p; b >>= 1;
}
return ans;
}
void desc(ll x, std::vector<int> &V) {
ll bd = floor(sqrt((double)x) + 0.5);
for(ll i = 2; i <= bd; i ++) {
if(x % i == 0LL) {
V.push_back(i);
while(x % i == 0LL) x /= i;
}
}
if(x > 1LL) V.push_back(int(x));
}
ll find_g(ll p, ll phi, std::vector<int> &V) {
if(p == 2LL) return 1;
for(ll i = 2; i < p; i ++) {
bool ok = true;
for(int j = 0; j < V.size(); j ++) {
ll c = phi / (ll)V[j];
if(pow_mod(i, c, p) == 1LL) {
ok = false; break;
}
}
if(ok) return i;
}
return -1LL;
}
ll bsgs(ll a, ll b, ll p) {
if(a == 0LL) {
return (b == 0LL) ? 1LL : -1LL;
}
int bd = ceil(sqrt((double)p));
std::tr1::unordered_map<ll, ll> ma;
ll blk = 1LL;
for(int i = 0; i < bd; i ++) {
if(!ma.count(blk)) ma[blk] = i;
blk = blk * a % p;
}
ll bs = 1LL; blk = inv(blk, p);
for(int i = 0; (ll)i * (ll)bd < p; i ++) {
ll th = b * bs % p;
if(ma.count(th)) return ma[th] + i * bd;
bs = bs * blk % p;
}
assert(false);
return -1;
}
ll equation(ll a, ll b, ll p) {
ll ret = gcd(a, p);
if(b % ret != 0LL) return 0;
else return ret;
}
ll solve(ll a, ll b, ll mod, ll p, ll c) {
if(b == 0LL) {
ll ret = ceil((double(c)) / (double(a)));
return pow_mod(p, c - ret, 2000000007LL);
} else {
if(b % p == 0LL) {
ll nc = 0;
while(b % p == 0LL) nc ++, b /= p, mod /= p;
if(nc % a != 0LL) return 0LL;
ll t = nc / a;
return solve(a, b, mod, p, c - nc) * pow_mod(p, (a - 1LL) * t, 2000000007LL);
} else {
ll phi = mod / p * (p - 1LL);
std::vector<int> d_phi; desc(phi, d_phi);
ll g = find_g(mod, phi, d_phi);
return equation(a, bsgs(g, b, mod), phi);
}
}
}
int main() {
int T; scanf("%d", &T);
while(T --) {
int a, b, k; scanf("%d%d%d", &a, &b, &k);
k = 2 * k + 1;
int bd = floor(sqrt((double)k) + 0.5);
int ans = 1;
for(int i = 2; i <= bd; i ++) {
if(k % i == 0) {
int c = 0, mod = 1;
while(k % i == 0) k /= i, c ++, mod *= i;
ans *= solve(a, b % mod, mod, i, c);
}
}
if(k > 1) ans *= solve(a, b % k, k, k, 1);
printf("%dn", ans);
}
return 0;
}
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