B. The Child and Settime limit per test1 secondmemory limit per test256 megabytesinputstandard inputoutputstandard outputAt 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 2k 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?InputThe first line contains two integers: sum, limit (1 ≤ sum, limit ≤ 105).OutputIn 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.ExamplesInput5 5Output24 5Input4 3Output32 3 1Input5 1Output-1NoteIn 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.
Input5 5
Output24 5
['bitmasks', 'greedy', 'implementation', 'sortings', '*1500']