#include <bits/stdc++.h>
using namespace std;
const int M = 1e9 + 7;
void _print(vector<vector<long long>> v) {
  for (int i = 0; i < v.size(); ++i) {
    vector<long long> b = v[i];
    cerr << "[ ";
    for (int j = 0; j < b.size(); ++j) {
      cerr << v[i][j] << " ";
    }
    cerr << "]";
    cerr << endl;
  }
}
void _print(vector<long long> v) {
  cerr << "["
       << " ";
  for (long long i : v) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<bool> v) {
  cerr << "["
       << " ";
  for (long long i : v) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<pair<long long, long long>> v) {
  cerr << "[" << endl;
  for (auto i : v) {
    cerr << i.first << " " << i.second << endl;
  }
  cerr << "]";
}
void _print(map<long long, long long> mp) {
  cerr << "[" << endl;
  for (auto i : mp) {
    cerr << i.first << " " << i.second << endl;
  }
  cerr << "]";
}
void _print(unordered_map<long long, long long> mp) {
  cerr << "[" << endl;
  for (auto i : mp) {
    cerr << i.first << " " << i.second << endl;
  }
  cerr << "]";
}
void _print(set<long long> s) {
  cerr << "["
       << " ";
  for (auto i : s) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(multiset<long long> s) {
  cerr << "["
       << " ";
  for (auto i : s) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(unordered_set<long long> s) {
  cerr << "["
       << " ";
  for (auto i : s) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<int> v) {
  cerr << "["
       << " ";
  for (int i : v) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<string> v) {
  cerr << "["
       << " ";
  for (auto i : v) {
    cerr << i << endl;
  }
  cerr << "]";
}
void _print(pair<long long, long long> a) {
  cerr << a.first << " " << a.second;
}
void _print(int a) { cerr << a; }
void _print(long long a) { cerr << a; }
void _print(string a) { cerr << a; }
void _print(bool a) { cerr << a; }
void _print(char a) { cerr << a; }
void _print(double a) { cerr << a; }
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long bpow(long long a, long long b, long long mod = M) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return res;
}
bool isSorted(vector<long long> &a) {
  long long f = 1;
  for (int i = 0; i < a.size(); ++i) {
    if (a[i] > a[i + 1]) {
      f = 0;
      break;
    }
  }
  return f;
}
void solve() {
  long long a, b;
  cin >> a >> b;
  double k = (double)(a + b) / 2;
  long long p = ceil(k);
  long long q = floor(k);
  vector<long long> ans;
  for (int i = 0; i <= p; ++i) {
    long long y = a - (p - i);
    if (y >= 0 and y <= q) ans.push_back(i + y);
  }
  for (int i = 0; i <= q; ++i) {
    long long y = a - (q - i);
    if (y >= 0 and y <= p) ans.push_back(i + y);
  }
  sort(ans.begin(), ans.end());
  vector<long long> ans1;
  ans1.push_back(ans[0]);
  for (int i = 1; i < ans.size(); ++i) {
    if (ans[i] != ans[i - 1]) ans1.push_back(ans[i]);
  }
  cout << ans1.size() << endl;
  for (int i = 0; i < ans1.size(); ++i) {
    cout << ans1[i] << " ";
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    solve();
  }
}

### Prompt

In Cpp, your task is to solve the following problem:

Alice and Borys are playing tennis.

A tennis match consists of games. In each game, one of the players is serving and the other one is receiving.

Players serve in turns: after a game where Alice is serving follows a game where Borys is serving, and vice versa.

Each game ends with a victory of one of the players. If a game is won by the serving player, it's said that this player holds serve. If a game is won by the receiving player, it's said that this player breaks serve.

It is known that Alice won a games and Borys won b games during the match. It is unknown who served first and who won which games.

Find all values of k such that exactly k breaks could happen during the match between Alice and Borys in total.

Input

Each test contains multiple test cases. The first line contains the number of test cases t (1 ≤ t ≤ 10^3). Description of the test cases follows.

Each of the next t lines describes one test case and contains two integers a and b (0 ≤ a, b ≤ 10^5; a + b > 0) — the number of games won by Alice and Borys, respectively.

It is guaranteed that the sum of a + b over all test cases does not exceed 2 ⋅ 10^5.

Output

For each test case print two lines.

In the first line, print a single integer m (1 ≤ m ≤ a + b + 1) — the number of values of k such that exactly k breaks could happen during the match.

In the second line, print m distinct integers k_1, k_2, …, k_m (0 ≤ k_1 < k_2 < … < k_m ≤ a + b) — the sought values of k in increasing order.

Example

Input


3
2 1
1 1
0 5


Output


4
0 1 2 3
2
0 2
2
2 3

Note

In the first test case, any number of breaks between 0 and 3 could happen during the match: 

  * Alice holds serve, Borys holds serve, Alice holds serve: 0 breaks; 
  * Borys holds serve, Alice holds serve, Alice breaks serve: 1 break; 
  * Borys breaks serve, Alice breaks serve, Alice holds serve: 2 breaks; 
  * Alice breaks serve, Borys breaks serve, Alice breaks serve: 3 breaks. 



In the second test case, the players could either both hold serves (0 breaks) or both break serves (2 breaks).

In the third test case, either 2 or 3 breaks could happen: 

  * Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve: 2 breaks; 
  * Borys breaks serve, Borys holds serve, Borys breaks serve, Borys holds serve, Borys breaks serve: 3 breaks. 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const int M = 1e9 + 7;
void _print(vector<vector<long long>> v) {
  for (int i = 0; i < v.size(); ++i) {
    vector<long long> b = v[i];
    cerr << "[ ";
    for (int j = 0; j < b.size(); ++j) {
      cerr << v[i][j] << " ";
    }
    cerr << "]";
    cerr << endl;
  }
}
void _print(vector<long long> v) {
  cerr << "["
       << " ";
  for (long long i : v) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<bool> v) {
  cerr << "["
       << " ";
  for (long long i : v) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<pair<long long, long long>> v) {
  cerr << "[" << endl;
  for (auto i : v) {
    cerr << i.first << " " << i.second << endl;
  }
  cerr << "]";
}
void _print(map<long long, long long> mp) {
  cerr << "[" << endl;
  for (auto i : mp) {
    cerr << i.first << " " << i.second << endl;
  }
  cerr << "]";
}
void _print(unordered_map<long long, long long> mp) {
  cerr << "[" << endl;
  for (auto i : mp) {
    cerr << i.first << " " << i.second << endl;
  }
  cerr << "]";
}
void _print(set<long long> s) {
  cerr << "["
       << " ";
  for (auto i : s) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(multiset<long long> s) {
  cerr << "["
       << " ";
  for (auto i : s) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(unordered_set<long long> s) {
  cerr << "["
       << " ";
  for (auto i : s) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<int> v) {
  cerr << "["
       << " ";
  for (int i : v) {
    cerr << i << " ";
  }
  cerr << "]";
}
void _print(vector<string> v) {
  cerr << "["
       << " ";
  for (auto i : v) {
    cerr << i << endl;
  }
  cerr << "]";
}
void _print(pair<long long, long long> a) {
  cerr << a.first << " " << a.second;
}
void _print(int a) { cerr << a; }
void _print(long long a) { cerr << a; }
void _print(string a) { cerr << a; }
void _print(bool a) { cerr << a; }
void _print(char a) { cerr << a; }
void _print(double a) { cerr << a; }
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return (a * b) / gcd(a, b); }
long long bpow(long long a, long long b, long long mod = M) {
  long long res = 1;
  while (b) {
    if (b & 1) res = (res * a) % mod;
    a = (a * a) % mod;
    b >>= 1;
  }
  return res;
}
bool isSorted(vector<long long> &a) {
  long long f = 1;
  for (int i = 0; i < a.size(); ++i) {
    if (a[i] > a[i + 1]) {
      f = 0;
      break;
    }
  }
  return f;
}
void solve() {
  long long a, b;
  cin >> a >> b;
  double k = (double)(a + b) / 2;
  long long p = ceil(k);
  long long q = floor(k);
  vector<long long> ans;
  for (int i = 0; i <= p; ++i) {
    long long y = a - (p - i);
    if (y >= 0 and y <= q) ans.push_back(i + y);
  }
  for (int i = 0; i <= q; ++i) {
    long long y = a - (q - i);
    if (y >= 0 and y <= p) ans.push_back(i + y);
  }
  sort(ans.begin(), ans.end());
  vector<long long> ans1;
  ans1.push_back(ans[0]);
  for (int i = 1; i < ans.size(); ++i) {
    if (ans[i] != ans[i - 1]) ans1.push_back(ans[i]);
  }
  cout << ans1.size() << endl;
  for (int i = 0; i < ans1.size(); ++i) {
    cout << ans1[i] << " ";
  }
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  long long t;
  cin >> t;
  while (t--) {
    solve();
  }
}

```