201454: [AtCoder]ARC145 E - Adjacent XOR
Description
Score : $800$ points
Problem Statement
You are given two sequences, each of length $N$, consisting of non-negative integers: $ A=(A_1,A_2,\ldots,A_{N})$ and $B=(B_1,B_2,\ldots,B_{N})$.
Determine whether it is possible to make $A$ equal to $B$ by performing the operation below at most $70000$ times. If it is possible, present a specific sequence of operations that achieves it.
- Choose an integer $ K\ (1\le K \le N)$. For every integer $i\ (2\leq i \leq K)$, simultaneously replace the value of $A_i$ with $ A_{i-1} \oplus A_i$.
Here, $\oplus$ denotes bitwise $\mathrm{XOR}$.
What is bitwise $\mathrm{XOR}$?
The bitwise $\mathrm{XOR}$ of non-negative integers $A$ and $B$, $A\oplus B$, is defined as follows:
- When $A\oplus B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if exactly one of the digits in that place of $A$ and $B$ are $1$, and $0$ otherwise.
For example, $3\oplus 5 = 6$ (in base two: $011\oplus 101 = 110$).
Constraints
- $2 \leq N \leq 1000$
- $0 \leq A_i, B_i < 2^{60}$
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
$N$ $A_1$ $A_2$ $\ldots$ $A_N$ $B_1$ $B_2$ $\ldots$ $B_N$
Output
If it is impossible to make $A$ equal to $B$ in at most $70000$ operations, print No. If it is possible, print a sequence of operations that achieves it in the following format, where $M$ is the number of operations, and $K_i$ is the integer chosen in the $i$-th operation:
Yes $M$ $K_1$ $K_2$ $\ldots$ $K_M$
If multiple solutions exist, any of them will be accepted.
Sample Input 1
3 1 2 0 1 2 3
Sample Output 1
Yes 2 2 3
In this output, the sequence $A$ is changed as follows:
- Initially: $A=(1, 2, 0)$.
- After the $1$-st operation: $A=(1, 3, 0)$.
- After the $2$-nd operation: $A=(1, 2, 3)$.
After the two operations, $A$ and $B$ are equal, achieving the objective.
Sample Input 2
2 10 100 1 0
Sample Output 2
No
Sample Input 3
2 1152921504606846975 0 1152921504606846975 0
Sample Output 3
Yes 0