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C. Subsequence Counting

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPikachu 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.

Input

The only line of input consists of two space separated integers *X* and *d* (1 ≤ *X*, *d* ≤ 10^{9}).

Output

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.

Examples

Input

10 5

Output

6

5 50 7 15 6 100

Input

4 2

Output

4

10 100 1000 10000

Note

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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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