Problem:
Score : 400 points

Problem Statement

We have N integers. The i-th integer is A_i.

Find \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

What is \mbox{ XOR }?

The XOR of integers A and B, A \mbox{ XOR } B, is defined as follows:

When A \mbox{ 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 \mbox{ XOR } 5 = 6. (In base two: 011 \mbox{ 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

Output

Print the value \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \mbox{ XOR } A_j), modulo (10^9+7).

Sample Input 1

3
1 2 3

Sample Output 1

6

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

Sample Input 2

10
3 1 4 1 5 9 2 6 5 3

Sample Output 2

237

Sample Input 3

10
3 14 159 2653 58979 323846 2643383 27950288 419716939 9375105820

Sample Output 3

103715602

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

Solution in Scala (2.11.7) (judge verdict: Time Limit Exceeded)

object Main extends scala.App {
    import java.util
    import scala.collection._
    import scala.collection.mutable.ListBuffer
    import scala.math._

    val mod = (pow(10.0, 9) + 7).toInt
    val sc = new java.util.Scanner(System.in)
    val N = sc.nextInt()

    val buf = ListBuffer.empty[Long]
    for (i <- 0 until N) {
        buf += sc.nextLong()
    }
    val ary = buf.toList

    var result = 0L
    for (i <- 0 until (N-1)) {
        for (j <- (i+1) until N) {
            result += (ary(i) ^ ary(j)) % mod
            result %= mod
        }
    }
    println(result)
}