Adjacent Replace

AtCoder

IDarc199_b

Time2000ms

Memory256MB

Difficulty—

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: $011 \oplus 101 = 110$). ## Constraints * $1\leq T\leq 50$ * $3\leq N\leq 60$ * $0\leq A_i,K\lt 2^{60}$ * All input values are integers. ## Input 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: $N$ $K$ $A_1$ $A_2$ $\ldots$ $A_N$ [samples]

Samples

Input #1

Output #1

Yes
2
2 1
Yes
3
1 1 1
No
Yes
0

Yes
4
2 3 2 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.

API Response (JSON)

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      "statement_type": "Markdown",
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