AT_arc199_b [ARC199B] Adjacent Replace

You are given a sequence of non-negative integers of length $ N $ : $ A=(A_1,A_2,\ldots,A_N) $ and a non-negative integer $ K $ . Determine whether it is possible to make $ A_1=K $ by performing the following operation at most $ 10^4 $ times: - Choose an integer $ i\ (1\leq i\leq N-1) $ . Let $ x=A_i\oplus A_{i+1} $ , then replace both $ A_i,A_{i+1} $ with $ x $ . Here, $ \oplus $ denotes the bitwise XOR operation. If possible, output one such sequence of operations. You are given $ T $ test cases, so solve each of them. What is bitwise XOR operation? The bitwise XOR of non-negative integers $ A, B $ , denoted $ A \oplus B $ , is defined as follows: - When $ A \oplus B $ is written in binary, the digit in the $ 2^k $ ( $ k \geq 0 $ ) place is $ 1 $ if exactly one of $ A, B $ has $ 1 $ in the $ 2^k $ place when written in binary, and $ 0 $ otherwise. For example, $ 3 \oplus 5 = 6 $ (in binary: $ 011 \oplus 101 = 110 $ ).

The input is given from Standard Input in the following format: > $ T $ $ \mathrm{case}_1 $ $ \mathrm{case}_2 $ $ \vdots $ $ \mathrm{case}_T $ Each test case is given in the following format: > $ N $ $ K $ $ A_1 $ $ A_2 $ $ \ldots $ $ A_N $

Output your solutions for $ \mathrm{case}_1,\mathrm{case}_2,\ldots,\mathrm{case}_T $ in order in the following format: If it is impossible to make $ A_1=K $ by performing the operation at most $ 10^4 $ times, output `No`. If possible, output the sequence of operations in the following format: > Yes $ M $ $ i_1 $ $ i_2 $ $ \ldots $ $ i_M $ Here, $ M $ is the number of operations, and $ i_j\ (1\leq j\leq M) $ represents the integer $ i $ chosen in the $ j $ -th operation. You need to satisfy $ 0\leq M\leq 10^4, 1\leq i_j\leq N-1 $ . If there are multiple sequences of operations that satisfy the conditions, any of them will be considered correct.

### Sample Explanation 1 For the first test case, you can make $ A_1=5 $ by performing the operations as follows: 1. Choose $ i=2 $ . $ A $ becomes $ (2,7,7) $ . 2. Choose $ i=1 $ . $ A $ becomes $ (5,5,7) $ . For the second test case, you can make $ A_1=0 $ by performing the operations as follows: 1. Choose $ i=1 $ . $ A $ becomes $ (1,1,4) $ . 2. Choose $ i=1 $ . $ A $ becomes $ (0,0,4) $ . 3. Choose $ i=1 $ . $ A $ becomes $ (0,0,4) $ . For the third test case, it is impossible to make $ A_1=8 $ with at most $ 10^4 $ operations. ### Constraints - $ 1\leq T\leq 50 $ - $ 3\leq N\leq 60 $ - $ 0\leq A_i,K\lt 2^{60} $ - All input values are integers.