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 2 n - 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 10 18 . Note the number of elements in the output array should not be more than 10 4 . If no answer is possible, print - 1 . The only line of input consists of two space separated integers X and d ( 1 ≤ X , d ≤ 10 9 ). Output should consist of two lines. First line should contain a single integer n ( 1 ≤ n ≤ 10 000 )— the number of integers in the final array. Second line should consist of n space separated integers — a 1 , a 2 , ... , a n ( 1 ≤ a i < 10 18 ). If there is no answer, print a single integer -1 . If there are multiple answers, print any of them. In the output of the first example case, the remaining subsequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 5 are 5, 5, 7, 5, 6, 5, 7, 6, 50, 7, 7, 6, 15, 6, 100 . There are 10 of them. Hence, the array 5, 50, 7, 15, 6, 100 is valid. Similarly, in the output of the second example case, the remaining sub-sequences after removing those with Maximum_element_of_the_subsequence - Minimum_element_of_subsequence ≥ 2 are 10, 100, 1000, 10000 . There are 4 of them. Hence, the array 10, 100, 1000, 10000 is valid.