AT_arc208_b [ARC208B] Sum of Mod

You are given positive integers $ N $ and $ K $ . Find one length- $ N $ sequence of positive integers $ A=(A_1,A_2,\ldots,A_N) $ with the minimum value of $ A_N $ among the ones that satisfy all of the following conditions. - $ A $ is non-decreasing. That is, $ A_i \le A_{i+1} $ for $ 1\le i\le N-1 $ . - $ \displaystyle \sum_{i=1}^{N-1} (A_{i+1} \bmod A_i)=K $ . You are given $ T $ test cases; solve each of them.

The input is given from Standard Input in the following format: > $ T $ $ \text{case}_1 $ $ \text{case}_2 $ $ \vdots $ $ \text{case}_T $ Each test case is given in the following format: > $ N $ $ K $

Output the answers for each test case in order, separated by newlines. For each test case, print $ A $ that satisfies all conditions and has the minimum value of $ A_N $ in the following format: > $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ If there are multiple $ A $ that satisfy all conditions and have the minimum value of $ A_N $ , any of them will be accepted.

### Sample Explanation 1 Consider the first test case. $ A=(1,2,3,4,5) $ is non-decreasing and satisfies $ \displaystyle \sum_{i=1}^{N-1} (A_{i+1} \bmod A_i) = (2\bmod 1) + (3\bmod 2) + (4\bmod 3) + (5\bmod 4)=3=K $ , so it satisfies all conditions. There does not exist an $ A $ that satisfies all conditions and has a value of $ A_N $ less than $ 5 $ , so printing $ A=(1,2,3,4,5) $ will be accepted. Other than this, printing $ A=(2,3,4,5,5) $ or $ A=(2,3,3,5,5) $ will also be accepted. ### Constraints - $ 1\le T \le 10^5 $ - $ 2\le N \le 2\times 10^5 $ - The sum of $ N $ over all test cases is at most $ 2\times 10^5 $ . - $ 1\le K\le 10^9 $ - All input values are integers.