XXOR

AtCoder

IDabc117_d

Time2000ms

Memory256MB

Difficulty—

You are given $N$ non-negative integers $A_1, A_2, ..., A_N$ and another non-negative integer $K$. For a integer $X$ between $0$ and $K$ (inclusive), let $f(X) = (X$ XOR $A_1)$ $+$ $(X$ XOR $A_2)$ $+$ $...$ $+$ $(X$ XOR $A_N)$. Here, for non-negative integers $a$ and $b$, $a$ XOR $b$ denotes the bitwise exclusive OR of $a$ and $b$. Find the maximum value of $f$. What is XOR? The bitwise exclusive OR of $a$ and $b$, $X$, is defined as follows: * When $X$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if, when written in base two, exactly one of $A$ and $B$ has $1$ in the $2^k$'s place, and $0$ otherwise. For example, $3$ XOR $5 = 6$. (When written in base two: $011$ XOR $101 = 110$.) ## Constraints * All values in input are integers. * $1 \leq N \leq 10^5$ * $0 \leq K \leq 10^{12}$ * $0 \leq A_i \leq 10^{12}$ ## Input Input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3 7
1 6 3

Output #1

14

The maximum value is: $f(4) = (4$ XOR $1) + (4$ XOR $6) + (4$ XOR $3) = 5 + 2 + 7 = 14$.

Input #2

4 9
7 4 0 3

Output #2

Input #3

1 0
1000000000000

Output #3

1000000000000

API Response (JSON)

{
  "problem": {
    "name": "XXOR",
    "description": {
      "content": "You are given $N$ non-negative integers $A_1, A_2, ..., A_N$ and another non-negative integer $K$. For a integer $X$ between $0$ and $K$ (inclusive), let $f(X) = (X$ XOR $A_1)$ $+$ $(X$ XOR $A_2)$ $+$",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc117_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given $N$ non-negative integers $A_1, A_2, ..., A_N$ and another non-negative integer $K$.\nFor a integer $X$ between $0$ and $K$ (inclusive), let $f(X) = (X$ XOR $A_1)$ $+$ $(X$ XOR $A_2)$ $+$...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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