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 was equal to
  sum; here lowbit(x) equals
  2^k 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?

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

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.

5 5

2

4 5

4 3

3

2 3 1

5 1