201373: [AtCoder]ARC137 D - Prefix XORs
Memory Limit：1024 MB
Time Limit：4 S
Judge Style：Text Compare
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Solved：0
Description
Score : $700$ points
Problem Statement
You are given an integer sequence of length $N$: $A=(A_1,A_2,\cdots,A_N)$, and an integer $M$.
For each $k=1,2,\cdots,M$, find the value of $A_N$ after doing the operation below $k$ times.
- For every $i$ ($1 \leq i \leq N$), simultaneously, replace the value of $A_i$ with $A_1 \oplus A_2 \oplus \cdots \oplus A_i$.
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 $A$ and $B$ is $1$, and $0$ otherwise.
Generally, the bitwise $\mathrm{XOR}$ of $k$ integers $p_1, p_2, p_3, \dots, p_k$ is defined as $(\dots ((p_1 \oplus p_2) \oplus p_3) \oplus \dots \oplus p_k)$. We can prove that this value does not depend on the order of $p_1, p_2, p_3, \dots p_k$.
Constraints
- $1 \leq N \leq 10^6$
- $1 \leq M \leq 10^6$
- $0 \leq A_i < 2^{30}$
- All values in input are integers.
Input
Input is given from Standard Input in the following format:
$N$ $M$ $A_1$ $A_2$ $\cdots$ $A_N$
Output
Print the answers for respective values of $k$, separated by spaces.
Sample Input 1
3 2 2 1 3
Sample Output 1
0 1
Each operation changes $A$ as follows.
- Initially: $A=(2,1,3)$.
- After the first operation: $A=(2,3,0)$.
- After the second operation: $A=(2,1,1)$.
Sample Input 2
10 12 721939838 337089195 171851101 1069204754 348295925 77134863 839878205 89360649 838712948 918594427
Sample Output 2
716176219 480674244 678890528 642764255 259091950 663009497 942498522 584528336 364872846 145822575 392655861 844652404