Prefix XORs

AtCoder

IDarc137_d

Time4000ms

Memory256MB

Difficulty—

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. For example, we have $3 \oplus 5 = 6$ (in base two: $011 \oplus 101 = 110$). 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: $N$ $M$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

3 2
2 1 3

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: $A=(2,1,1)$.

Input #2

10 12
721939838 337089195 171851101 1069204754 348295925 77134863 839878205 89360649 838712948 918594427

Output #2

716176219 480674244 678890528 642764255 259091950 663009497 942498522 584528336 364872846 145822575 392655861 844652404

API Response (JSON)

{
  "problem": {
    "name": "Prefix XORs",
    "description": {
      "content": "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 ev",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 4000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc137_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given an integer sequence of length $N$: $A=(A_1,A_2,\\cdots,A_N)$, and an integer $M$.\nFor each $k=1,2,\\cdots,M$, find the value of $A_N$ after doing the operation below $k$ times.\n\n*   For ev...",
      "is_translate": false,
      "language": "English"
    }
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}

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