A9532 | The Child and Set

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, $lowbit(10010_{2})=10_{2},lowbit(10001_{2})=1_{2},lowbit(10000_{2})=10000_{2}$ (binary representation).

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

The first line contains two integers: $sum,limit$ $(1<=sum,limit<=10^{5})$ .

In the first line print an integer $n$ $(1<=n<=10^{5})$ , 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.