CF1957B A BIT of a Construction

Given integers $ n $ and $ k $ , construct a sequence of $ n $ non-negative (i.e. $ \geq 0 $ ) integers $ a_1, a_2, \ldots, a_n $ such that 1. $ \sum\limits_{i = 1}^n a_i = k $ 2. The number of $ 1 $ s in the binary representation of $ a_1 | a_2 | \ldots | a_n $ is maximized, where $ | $ denotes the [bitwise OR operation](https://en.wikipedia.org/wiki/Bitwise_operation#OR).

The first line contains a single integer $ t $ ( $ 1 \leq t \leq 10^4 $ ) — the number of test cases. The only line of each test case contains two integers $ n $ and $ k $ ( $ 1 \leq n \leq 2 \cdot 10^5 $ , $ 1 \leq k \leq 10^9 $ ) — the number of non-negative integers to be printed and the sum respectively. It is guaranteed that the sum of $ n $ over all test cases does not exceed $ 2 \cdot 10^5 $ .

For each test case, output a sequence $ a_1, a_2, \ldots, a_n $ on a new line that satisfies the conditions given above. If there are multiple solutions, print any of them.

In the first test case, we have to print exactly one integer, hence we can only output $ 5 $ as the answer. In the second test case, we output $ 1, 2 $ which sum up to $ 3 $ , and $ 1 | 2 = (11)_2 $ has two $ 1 $ s in its binary representation, which is the maximum we can achieve in these constraints. In the fourth test case, we output $ 3, 1, 1, 32, 2, 12 $ which sum up to $ 51 $ , and $ 3 | 1 | 1 | 32 | 2 | 12 = (101\,111)_2 $ has five $ 1 $ s in its binary representation, which is the maximum we can achieve in these constraints.