CF960C Subsequence Counting

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

Output should consist of two lines. First line should contain a single integer $ n $ ( $ 1

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.