Codeforces div.2 B. The Child and Set

题目例如以下：

B. The Child and Set

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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?

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.

Sample test(s)

Input

5 5

Output

2
4 5

Input

4 3

Output

3
2 3 1

Input

5 1

Output

-1

这道题求出二进制的低位（从最先出现1的位置截断），事实上就是位运算。恰好我不熟悉位运算。罪过啊。。

。于是恶补了位运算，求二进制低位用i&-i,求最后以为i&1，左移i<<1,右移i>>1,然后从limit枚举。假设小于sum，就增加答案中.

自己的代码太丑了。粘贴一下别人的美丽的代码：