Xor Sum 4

AtCoder

IDabc147_d

Time2000ms

Memory256MB

Difficulty—

We have $N$ integers. The $i$\-th integer is $A_i$. Find $\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \text{ XOR } A_j)$, modulo $(10^9+7)$. What is $\text{ XOR }$?The XOR of integers $A$ and $B$, $A \text{ XOR } B$, is defined as follows: * When $A \text{ XOR } B$ is written in base two, the digit in the $2^k$'s place ($k \geq 0$) is $1$ if either $A$ or $B$, but not both, has $1$ in the $2^k$'s place, and $0$ otherwise. For example, $3 \text{ XOR } 5 = 6$. (In base two: $011 \text{ XOR } 101 = 110$.) ## Constraints * $2 \leq N \leq 3 \times 10^5$ * $0 \leq A_i < 2^{60}$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ $...$ $A_N$ [samples]

Samples

Input #1

3
1 2 3

Output #1

6

We have $(1\text{ XOR } 2)+(1\text{ XOR } 3)+(2\text{ XOR } 3)=3+2+1=6$.

Input #2

10
3 1 4 1 5 9 2 6 5 3

Output #2

Input #3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Output #3

103715602

Print the sum modulo $(10^9+7)$.

API Response (JSON)

{
  "problem": {
    "name": "Xor Sum 4",
    "description": {
      "content": "We have $N$ integers. The $i$\\-th integer is $A_i$. Find $\\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\text{ XOR } A_j)$, modulo $(10^9+7)$. What is $\\text{ XOR }$?The XOR of integers $A$ and $B$, $A \\text{",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc147_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have $N$ integers. The $i$\\-th integer is $A_i$.\nFind $\\sum_{i=1}^{N-1}\\sum_{j=i+1}^{N} (A_i \\text{ XOR } A_j)$, modulo $(10^9+7)$.\nWhat is $\\text{ XOR }$?The XOR of integers $A$ and $B$, $A \\text{...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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