#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using qi = queue<int>;
using stki = stack<int>;
template <typename T>
using vec = vector<T>;
template <typename T>
using us = unordered_set<T>;
template <typename T>
using os = set<T>;
template <typename T>
using ms = multiset<T>;
template <typename T1, typename T2>
using um = unordered_map<T1, T2>;
template <typename T1, typename T2>
using om = map<T1, T2>;
template <typename T>
using pq = priority_queue<T>;
template <typename T>
using pqg = priority_queue<T, vec<T>, greater<T> >;
using vi = vec<int>;
using vpii = vec<pii>;
using vll = vec<ll>;
using vpll = vec<pll>;
using vb = vec<bool>;
const int INF = 0x3f3f3f3f;
const ll LLINF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1e9 + 7;
const int dir[8][2] = {{0, 1},  {0, -1}, {-1, 0},  {1, 0},
                       {-1, 1}, {1, -1}, {-1, -1}, {1, 1}};
struct Edge {
  int u, v, w;
};
namespace comfun {
template <typename T>
inline void cmax(T &u, T v) {
  u = max(u, v);
}
template <typename T>
inline void cmin(T &u, T v) {
  u = min(u, v);
}
template <typename T>
inline T lowbit(T x) {
  return x & (-x);
}
template <typename T>
inline T gcd(T a, T b) {
  if (a == 0) return b;
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <typename T>
inline T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
template <typename T1, typename T2>
inline T1 fast_pow(T1 a, T2 b) {
  if (b == 1) return a;
  if (b == 0) return 1;
  T1 tmp = fast_pow(a, b >> 1);
  if (b & 1)
    return tmp * tmp * a;
  else
    return tmp * tmp;
}
template <typename T1, typename T2, typename T3>
inline T1 fast_pow(T1 a, T2 b, T3 m) {
  if (b == 1) return a % m;
  if (b == 0) return 1;
  T1 tmp = fast_pow(a, b >> 1, m);
  if (b & 1)
    return tmp * tmp % m * a % m;
  else
    return tmp * tmp % m;
}
template <typename T>
inline bool is_prime(T x) {
  if (x == 1) return false;
  for (T i = 2; i * i <= x; i++)
    if (x % i == 0) return false;
  return true;
}
}  // namespace comfun
namespace debug {
template <typename T>
inline void debugArray(T *arr, int sz) {
  cout << "[";
  for (int i = 0; i < sz; i++) {
    cout << arr[i] << ", ";
  }
  cout << "]\n";
}
template <typename T>
inline void printArray(T *arr, int sz) {
  for (int i = 0; i < sz; i++) {
    cout << arr[i] << " ";
  }
  cout << "\n";
}
}  // namespace debug
namespace fast_io {
void read(int &number) {
  bool negative = false;
  int c;
  number = 0;
  c = getchar();
  if (c == '-') {
    negative = true;
    c = getchar();
  }
  for (; (c > 47 && c < 58); c = getchar()) number = number * 10 + c - 48;
  if (negative) number *= -1;
}
}  // namespace fast_io
using namespace comfun;
using namespace debug;
using namespace fast_io;
inline void init1() {}
inline void init2() {}
inline void solve() {
  int c, d;
  cin >> c >> d;
  if (c == d) {
    if (c == 0)
      cout << 0 << '\n';
    else
      cout << 1 << '\n';
    return;
  }
  int mid = (c + d) >> 1;
  if ((c + d) % 2 == 0)
    cout << 2 << '\n';
  else
    cout << -1 << '\n';
}
inline void setIO() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int main() {
  setIO();
  init1();
  srand(time(0));
  int t;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    if (0) cout << "Case #" << i << ": ";
    init2();
    solve();
  }
  string jack = "Jack is always within you";
  return 0;
}

### Prompt

Your challenge is to write a cpp solution to the following problem:

<image>

William has two numbers a and b initially both equal to zero. William mastered performing three different operations with them quickly. Before performing each operation some positive integer k is picked, which is then used to perform one of the following operations: (note, that for each operation you can choose a new positive integer k)

  1. add number k to both a and b, or 
  2. add number k to a and subtract k from b, or 
  3. add number k to b and subtract k from a. 



Note that after performing operations, numbers a and b may become negative as well.

William wants to find out the minimal number of operations he would have to perform to make a equal to his favorite number c and b equal to his second favorite number d.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^4). Description of the test cases follows.

The only line of each test case contains two integers c and d (0 ≤ c, d ≤ 10^9), which are William's favorite numbers and which he wants a and b to be transformed into.

Output

For each test case output a single number, which is the minimal number of operations which William would have to perform to make a equal to c and b equal to d, or -1 if it is impossible to achieve this using the described operations.

Example

Input


6
1 2
3 5
5 3
6 6
8 0
0 0


Output


-1
2
2
1
2
0

Note

Let us demonstrate one of the suboptimal ways of getting a pair (3, 5):

  * Using an operation of the first type with k=1, the current pair would be equal to (1, 1). 
  * Using an operation of the third type with k=8, the current pair would be equal to (-7, 9). 
  * Using an operation of the second type with k=7, the current pair would be equal to (0, 2). 
  * Using an operation of the first type with k=3, the current pair would be equal to (3, 5). 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using qi = queue<int>;
using stki = stack<int>;
template <typename T>
using vec = vector<T>;
template <typename T>
using us = unordered_set<T>;
template <typename T>
using os = set<T>;
template <typename T>
using ms = multiset<T>;
template <typename T1, typename T2>
using um = unordered_map<T1, T2>;
template <typename T1, typename T2>
using om = map<T1, T2>;
template <typename T>
using pq = priority_queue<T>;
template <typename T>
using pqg = priority_queue<T, vec<T>, greater<T> >;
using vi = vec<int>;
using vpii = vec<pii>;
using vll = vec<ll>;
using vpll = vec<pll>;
using vb = vec<bool>;
const int INF = 0x3f3f3f3f;
const ll LLINF = 0x3f3f3f3f3f3f3f3f;
const int MOD = 1e9 + 7;
const int dir[8][2] = {{0, 1},  {0, -1}, {-1, 0},  {1, 0},
                       {-1, 1}, {1, -1}, {-1, -1}, {1, 1}};
struct Edge {
  int u, v, w;
};
namespace comfun {
template <typename T>
inline void cmax(T &u, T v) {
  u = max(u, v);
}
template <typename T>
inline void cmin(T &u, T v) {
  u = min(u, v);
}
template <typename T>
inline T lowbit(T x) {
  return x & (-x);
}
template <typename T>
inline T gcd(T a, T b) {
  if (a == 0) return b;
  if (b == 0) return a;
  return gcd(b, a % b);
}
template <typename T>
inline T lcm(T a, T b) {
  return a / gcd(a, b) * b;
}
template <typename T1, typename T2>
inline T1 fast_pow(T1 a, T2 b) {
  if (b == 1) return a;
  if (b == 0) return 1;
  T1 tmp = fast_pow(a, b >> 1);
  if (b & 1)
    return tmp * tmp * a;
  else
    return tmp * tmp;
}
template <typename T1, typename T2, typename T3>
inline T1 fast_pow(T1 a, T2 b, T3 m) {
  if (b == 1) return a % m;
  if (b == 0) return 1;
  T1 tmp = fast_pow(a, b >> 1, m);
  if (b & 1)
    return tmp * tmp % m * a % m;
  else
    return tmp * tmp % m;
}
template <typename T>
inline bool is_prime(T x) {
  if (x == 1) return false;
  for (T i = 2; i * i <= x; i++)
    if (x % i == 0) return false;
  return true;
}
}  // namespace comfun
namespace debug {
template <typename T>
inline void debugArray(T *arr, int sz) {
  cout << "[";
  for (int i = 0; i < sz; i++) {
    cout << arr[i] << ", ";
  }
  cout << "]\n";
}
template <typename T>
inline void printArray(T *arr, int sz) {
  for (int i = 0; i < sz; i++) {
    cout << arr[i] << " ";
  }
  cout << "\n";
}
}  // namespace debug
namespace fast_io {
void read(int &number) {
  bool negative = false;
  int c;
  number = 0;
  c = getchar();
  if (c == '-') {
    negative = true;
    c = getchar();
  }
  for (; (c > 47 && c < 58); c = getchar()) number = number * 10 + c - 48;
  if (negative) number *= -1;
}
}  // namespace fast_io
using namespace comfun;
using namespace debug;
using namespace fast_io;
inline void init1() {}
inline void init2() {}
inline void solve() {
  int c, d;
  cin >> c >> d;
  if (c == d) {
    if (c == 0)
      cout << 0 << '\n';
    else
      cout << 1 << '\n';
    return;
  }
  int mid = (c + d) >> 1;
  if ((c + d) % 2 == 0)
    cout << 2 << '\n';
  else
    cout << -1 << '\n';
}
inline void setIO() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
}
int main() {
  setIO();
  init1();
  srand(time(0));
  int t;
  cin >> t;
  for (int i = 1; i <= t; i++) {
    if (0) cout << "Case #" << i << ": ";
    init2();
    solve();
  }
  string jack = "Jack is always within you";
  return 0;
}

```