#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e18;
const long long N = 1e5 + 7;
const int MOD = (int)1e9 + 7;
long long calc(long long i) {
  for (long long j = 0; j < 32; j++) {
    if (i & (1 << j)) return 1 << j;
  }
}
void solve() {
  long long n, m;
  cin >> n >> m;
  vector<pair<long long, long long> > v;
  long long sum = 0;
  for (long long i = 1; i < m + 1; i++) {
    sum += calc(i);
    v.push_back({calc(i), i});
  }
  sort(v.rbegin(), v.rend());
  if (sum < n) {
    cout << -1;
    return;
  }
  long long diff = sum - n;
  vector<long long> ans;
  for (long long i = 0; i < m; i++) {
    if (diff >= v[i].first) {
      diff -= v[i].first;
    } else
      ans.push_back(v[i].second);
  }
  n = ((int)(ans).size());
  cout << n << '\n';
  for (long long i = 0; i < n; i++) cout << ans[i] << " ";
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  while (t--) {
    solve();
  }
}

### Prompt

Please provide a Cpp coded solution to the problem described below:

At the children's day, the child came to Picks's house, and messed his house up. Picks was angry at him. A lot of important things were lost, in particular the favorite set of Picks.

Fortunately, Picks remembers something about his set S:

  * its elements were distinct integers from 1 to limit; 
  * the value of <image> was equal to sum; here lowbit(x) equals 2k where k is the position of the first one in the binary representation of x. For example, lowbit(100102) = 102, lowbit(100012) = 12, lowbit(100002) = 100002 (binary representation). 



Can you help Picks and find any set S, that satisfies all the above conditions?

Input

The first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).

Output

In the first line print an integer n (1 ≤ n ≤ 105), denoting the size of S. Then print the elements of set S in any order. If there are multiple answers, print any of them.

If it's impossible to find a suitable set, print -1.

Examples

Input

5 5


Output

2
4 5


Input

4 3


Output

3
2 3 1


Input

5 1


Output

-1

Note

In sample test 1: lowbit(4) = 4, lowbit(5) = 1, 4 + 1 = 5.

In sample test 2: lowbit(1) = 1, lowbit(2) = 2, lowbit(3) = 1, 1 + 2 + 1 = 4.

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e18;
const long long N = 1e5 + 7;
const int MOD = (int)1e9 + 7;
long long calc(long long i) {
  for (long long j = 0; j < 32; j++) {
    if (i & (1 << j)) return 1 << j;
  }
}
void solve() {
  long long n, m;
  cin >> n >> m;
  vector<pair<long long, long long> > v;
  long long sum = 0;
  for (long long i = 1; i < m + 1; i++) {
    sum += calc(i);
    v.push_back({calc(i), i});
  }
  sort(v.rbegin(), v.rend());
  if (sum < n) {
    cout << -1;
    return;
  }
  long long diff = sum - n;
  vector<long long> ans;
  for (long long i = 0; i < m; i++) {
    if (diff >= v[i].first) {
      diff -= v[i].first;
    } else
      ans.push_back(v[i].second);
  }
  n = ((int)(ans).size());
  cout << n << '\n';
  for (long long i = 0; i < n; i++) cout << ans[i] << " ";
  return;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  long long t = 1;
  while (t--) {
    solve();
  }
}

```