CF1965B Missing Subsequence Sum

You are given two integers $ n $ and $ k $ . Find a sequence $ a $ of non-negative integers of size at most $ 25 $ such that the following conditions hold. - There is no subsequence of $ a $ with a sum of $ k $ . - For all $ 1 \le v \le n $ where $ v \ne k $ , there is a subsequence of $ a $ with a sum of $ v $ . A sequence $ b $ is a subsequence of $ a $ if $ b $ can be obtained from $ a $ by the deletion of several (possibly, zero or all) elements, without changing the order of the remaining elements. For example, $ [5, 2, 3] $ is a subsequence of $ [1, 5, 7, 8, 2, 4, 3] $ . It can be shown that under the given constraints, a solution always exists.

The first line of the input contains a single integer $ t $ ( $ 1 \le t \le 1000 $ ) — the number of test cases. The description of the test cases follows. Each test case consists of a single line containing two integers $ n $ and $ k $ ( $ 2 \le n \le 10^6 $ , $ 1 \le k \le n $ ) — the parameters described above. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 10^7 $ .

The first line of output for each test case should contain a single integer $ m $ ( $ 1 \le m \le 25 $ ) — the size of your chosen sequence. The second line of output for each test case should contain $ m $ integers $ a_i $ ( $ 0 \le a_i \le 10^9 $ ) — the elements of your chosen sequence. If there are multiple solutions, print any.

In the first example, we just need a subsequence that adds up to $ 1 $ , but not one that adds up to $ 2 $ . So the array $ a=[1] $ suffices. In the second example, all elements are greater than $ k=1 $ , so no subsequence adds up to $ 1 $ . Every other integer between $ 1 $ and $ n $ is present in the array, so there is a subsequence of size $ 1 $ adding up to each of those numbers.