#include <bits/stdc++.h>
using namespace std;
const int maxn = (int)2e5 + 10;
int init[maxn], cnt[maxn];
int sum, limit, ans;
int lowbit(int x) { return x & (-x); }
bool find(int u) {
  if (cnt[u]) {
    cnt[u] -= 1;
    ans += 1;
    return 1;
  }
  if (u == 1) return 0;
  if (find(u >> 1) == 0) return 0;
  if (find(u >> 1) == 0) return 0;
  return 1;
}
int main() {
  scanf("%d%d", &sum, &limit);
  for (int i = 1; i <= limit; i++) {
    int val = lowbit(i);
    init[val] += 1;
    cnt[val] += 1;
  }
  for (int i = 20; i >= 0; i--)
    if ((sum >> i) & 1) {
      if (find(1 << i) == 0) {
        puts("-1");
        return 0;
      }
    }
  printf("%d\n", ans);
  for (int i = 1; i <= limit; i++) {
    int val = lowbit(i);
    if (cnt[val] != init[val]) {
      printf("%d ", i);
      cnt[val] += 1;
    }
  }
  return 0;
}

### Prompt

Your task is to create a Cpp solution to the following problem:

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 int maxn = (int)2e5 + 10;
int init[maxn], cnt[maxn];
int sum, limit, ans;
int lowbit(int x) { return x & (-x); }
bool find(int u) {
  if (cnt[u]) {
    cnt[u] -= 1;
    ans += 1;
    return 1;
  }
  if (u == 1) return 0;
  if (find(u >> 1) == 0) return 0;
  if (find(u >> 1) == 0) return 0;
  return 1;
}
int main() {
  scanf("%d%d", &sum, &limit);
  for (int i = 1; i <= limit; i++) {
    int val = lowbit(i);
    init[val] += 1;
    cnt[val] += 1;
  }
  for (int i = 20; i >= 0; i--)
    if ((sum >> i) & 1) {
      if (find(1 << i) == 0) {
        puts("-1");
        return 0;
      }
    }
  printf("%d\n", ans);
  for (int i = 1; i <= limit; i++) {
    int val = lowbit(i);
    if (cnt[val] != init[val]) {
      printf("%d ", i);
      cnt[val] += 1;
    }
  }
  return 0;
}

```