AT_arc220_a [ARC220A] Sum of Reciprocals of Squares

You are given a positive integer $ N $ . Determine whether there exists a sequence of positive integers $ A=(A_1,A_2,\ldots,A_N) $ satisfying all of the following conditions, and if so, find one such sequence. - $ 1\le A_i\le 10^6 $ - $ \displaystyle \sum_{i=1}^N \frac1{A_i^2}=1 $ 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 $

Output the answers for the test cases in order, separated by newlines. For each test case, if no $ A $ satisfying all conditions exists, output `No`. If an $ A $ satisfying all conditions exists, output it in the following format: > Yes $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ If multiple $ A $ satisfying all conditions exist, any of them will be accepted.

### Sample Explanation 1 Consider the first test case. For $ A=(2,2,2,2) $ , we have $ \displaystyle \sum_{i=1}^N\frac1{A_i^2}=\frac14+\frac14+\frac14+\frac14=1 $ , so we can confirm that the conditions are satisfied. ### Constraints - $ 1\le T\le 500 $ - $ 1\le N\le 10^5 $ - The sum of $ N $ over all test cases is at most $ 10^5 $ . - All input values are integers.