The Child and Set

1000ms

262144K

Description:

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 $\text{[math]}$ 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 Input:

5 5

Sample Output:

2
4 5

Sample Input:

4 3

Sample Output:

3
2 3 1

Sample Input:

5 1

Sample Output:

-1

Note:

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.

Informação

Provedor Codeforces

Código CF437B