#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }
#define COLOR(s) ("\x1b[" s "m")

////////////////////////////////////////////////////////////////////////////////
template <unsigned M_> struct ModInt {
  static constexpr unsigned M = M_;
  unsigned x;
  constexpr ModInt() : x(0U) {}
  constexpr ModInt(unsigned x_) : x(x_ % M) {}
  constexpr ModInt(unsigned long long x_) : x(x_ % M) {}
  constexpr ModInt(int x_) : x(((x_ %= static_cast<int>(M)) < 0) ? (x_ + static_cast<int>(M)) : x_) {}
  constexpr ModInt(long long x_) : x(((x_ %= static_cast<long long>(M)) < 0) ? (x_ + static_cast<long long>(M)) : x_) {}
  ModInt &operator+=(const ModInt &a) { x = ((x += a.x) >= M) ? (x - M) : x; return *this; }
  ModInt &operator-=(const ModInt &a) { x = ((x -= a.x) >= M) ? (x + M) : x; return *this; }
  ModInt &operator*=(const ModInt &a) { x = (static_cast<unsigned long long>(x) * a.x) % M; return *this; }
  ModInt &operator/=(const ModInt &a) { return (*this *= a.inv()); }
  ModInt pow(long long e) const {
    if (e < 0) return inv().pow(-e);
    ModInt a = *this, b = 1U; for (; e; e >>= 1) { if (e & 1) b *= a; a *= a; } return b;
  }
  ModInt inv() const {
    unsigned a = M, b = x; int y = 0, z = 1;
    for (; b; ) { const unsigned q = a / b; const unsigned c = a - q * b; a = b; b = c; const int w = y - static_cast<int>(q) * z; y = z; z = w; }
    assert(a == 1U); return ModInt(y);
  }
  ModInt operator+() const { return *this; }
  ModInt operator-() const { ModInt a; a.x = x ? (M - x) : 0U; return a; }
  ModInt operator+(const ModInt &a) const { return (ModInt(*this) += a); }
  ModInt operator-(const ModInt &a) const { return (ModInt(*this) -= a); }
  ModInt operator*(const ModInt &a) const { return (ModInt(*this) *= a); }
  ModInt operator/(const ModInt &a) const { return (ModInt(*this) /= a); }
  template <class T> friend ModInt operator+(T a, const ModInt &b) { return (ModInt(a) += b); }
  template <class T> friend ModInt operator-(T a, const ModInt &b) { return (ModInt(a) -= b); }
  template <class T> friend ModInt operator*(T a, const ModInt &b) { return (ModInt(a) *= b); }
  template <class T> friend ModInt operator/(T a, const ModInt &b) { return (ModInt(a) /= b); }
  explicit operator bool() const { return x; }
  bool operator==(const ModInt &a) const { return (x == a.x); }
  bool operator!=(const ModInt &a) const { return (x != a.x); }
  friend std::ostream &operator<<(std::ostream &os, const ModInt &a) { return os << a.x; }
};
////////////////////////////////////////////////////////////////////////////////

constexpr unsigned MO = 1000000007;
using Mint = ModInt<MO>;


constexpr int TR[4] = {0, 1, 3, 2};
constexpr int LIM = 1'000'010;

char S[LIM], T[LIM];
Int K;

int main() {
  vector<Mint> A(LIM);
  A[0] = 1;
  for (int i = 1; i < LIM; ++i) {
    A[i] = 4 * A[i - 1] + 1;
  }
  
  for (int numCases; ~scanf("%d", &numCases); ) { for (int caseId = 1; caseId <= numCases; ++caseId) {
    scanf("%s%s%lld", S, T, &K);
    const int SLen = strlen(S);
    const int TLen = strlen(T);
    reverse(S, S + SLen);
    reverse(T, T + TLen);
    
    const int E = (max(SLen, TLen) + 1) / 2;
    vector<int> xs(E, 0);
    for (int e = 0; e < SLen; ++e) xs[e >> 1] ^= (S[e] - '0') << (e & 1);
    for (int e = 0; e < TLen; ++e) xs[e >> 1] ^= (T[e] - '0') << (e & 1);
    
    int e0 = -1;
    for (int e = 0; e < E; ++e) if (xs[e]) {
      e0 = (~e0) ? -2 : e;
    }
// cerr<<"xs = "<<xs<<", e0 = "<<e0<<endl;
    
    int ans = 0;
    if (e0 == -1) {
      ans = ((Mint(4).pow(K) - 1) / 3 - 1).x;
    } else if (e0 >= 0) {
      if (K == 1) {
        ans = (A[e0] * TR[xs[e0]]).x;
      } else if (e0 >= 1 && K == 2) {
        ans = (A[e0] * (TR[xs[e0]] + 1) - 1).x;
      } else {
        ans = -1;
      }
    } else {
      if (K == 1) {
        Mint sum = 0;
        for (int e = 0; e < E; ++e) {
          sum += A[e] * TR[xs[e]];
        }
        ans = sum.x;
      } else {
        ans = -1;
      }
    }
    printf("%d\n", ans);
  }
#ifndef LOCAL
  break;
#endif
  }
  return 0;
}