AT_arc200_d [ARC200D] |A + A|

You are given positive integers $ M,K $ . Determine whether there exist a positive integer $ N $ and an integer sequence $ A=(A_1,A_2,\ldots, A_N) $ that satisfy all the following conditions, and if they exist, find one. - $ 1\le N\le M $ - $ 0\le A_i < M $ $ (1\le i\le N) $ - There are exactly $ K $ integers $ 0\le k < M $ such that there exists a pair of indices $ (i,j) $ satisfying $ k\equiv A_i+A_j \pmod M $ . You are given $ T $ test cases, so find the answer for each.

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: > $ M $ $ K $

Output your solutions for the test cases in order, separated by newlines. For each test case, if there are no $ N,A $ that satisfy all conditions, output `No`. Otherwise, output $ N $ and $ A $ that satisfy all conditions in the following format: > Yes $ N $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $ If there are multiple $ N $ and $ A $ that satisfy the conditions, you may output any of them.

### Sample Explanation 1 For the first test case, if we set $ A=(3,1,4) $ , then - $ k=0 $ : Setting $ (i,j)=(1,1) $ , we have $ 0\equiv 3+3\pmod 6 $ . - $ k=1 $ : Setting $ (i,j)=(1,3) $ , we have $ 1\equiv 3+4\pmod 6 $ . - $ k=2 $ : Setting $ (i,j)=(3,3) $ , we have $ 2\equiv 4+4\pmod 6 $ . - $ k=3 $ : There is no pair of indices $ (i,j) $ that satisfies the condition. - $ k=4 $ : Setting $ (i,j)=(1,2) $ , we have $ 4\equiv 3+1\pmod 6 $ . - $ k=5 $ : Setting $ (i,j)=(2,3) $ , we have $ 5\equiv 1+4\pmod 6 $ . Thus, there are exactly $ 5 $ values of $ 0\le k < 6 $ that satisfy the condition. ### Constraints - $ 1\le T\le 2\times 10^5 $ - $ 1\le K\le M\le 2\times 10^5 $ - The sum of $ M $ over all test cases is at most $ 2\times 10^5 $ . - All input values are integers.