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?

输入描述:

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

输出描述:

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.

备注:

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.