Codeforces div.2 B. The Child and Set

題目如下：

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

這道題求出二進制的低位（從最先出現1的位置截斷），其實就是位運算，恰好我不熟悉位運算，罪過啊。。。於是惡補了位運算，求二進制低位用i&-i,求最後以為i&1，左移i<<1,右移i>>1,然後從limit枚舉，如果小於sum，就加入答案中.

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