Pikachu had an array with him. He wrote down all the non-empty subsequences of the array on paper. Note that an array of size n has 2n - 1 non-empty subsequences in it.

Pikachu being mischievous as he always is, removed all the subsequences in which Maximum_element_of_the_subsequence  -  Minimum_element_of_subsequence  ≥ d

Pikachu was finally left with X subsequences.

However, he lost the initial array he had, and now is in serious trouble. He still remembers the numbers X and d. He now wants you to construct any such array which will satisfy the above conditions. All the numbers in the final array should be positive integers less than 1018.

Note the number of elements in the output array should not be more than 104. If no answer is possible, print  - 1.

题目大意

x,d<=1e9

Examples
input
10 5
output
6
5 50 7 15 6 100

input
4 2
output
4
10 100 1000 10000

2的幂次加和的形式

$$x-=2^n-1$$

$$nownum+=(2*d)$$(这个随意)