AT_arc221_e [ARC221E] Two Increasing Sequences

You are given a positive integer $ N $ , a positive integer $ X $ , and a permutation $ P=(P_1,P_2,\ldots,P_N) $ of $ (1,2,\ldots,N) $ . Only $ X $ is given in binary, while $ N $ and the elements of $ P $ are given in decimal. Determine whether there exist sequences of non-negative integers $ A=(A_1,A_2,\ldots,A_N) $ and $ B=(B_1,B_2,\ldots,B_N) $ satisfying all of the following conditions. - Both $ A $ and $ B $ are strictly increasing sequences. - $ A_{P_i}=B_i \oplus X $ holds for $ i=1,2,\ldots,N $ . Here, the binary operator $ \oplus $ denotes the bitwise XOR of non-negative integers. 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 $ $ X $ $ P_1 $ $ P_2 $ $ \ldots $ $ P_N $

Output the answers for the test cases in order, separated by newlines. For each test case, output `Yes` if there exist $ A $ and $ B $ satisfying all the conditions, and `No` otherwise.

### Sample Explanation 1 For the first test case, for example, $ A=(2,3,5,7) $ and $ B=(0,2,6,7) $ satisfy the conditions. ### Constraints - $ 1\le T\le 10^5 $ - $ 2\le N\le 2\times 10^5 $ - $ 1\le X < 2^{10^6} $ - $ P $ is a permutation of $ (1,2,\ldots,N) $ . - The sum of $ N $ over all test cases is at most $ 2\times 10^5 $ . - The sum of the number of digits of $ X $ in binary over all test cases is at most $ 10^6 $ . - $ T,N,P_i $ are given in decimal. - $ X $ is given in binary without leading zeros. - All input values are integers.