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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
	"strings"
)

var mod uint64 = 1000000007

func main() {
	var n uint64
	fmt.Scan(&n)

	NewReader(int(n))
	a := ReadInts64(" ")

	var ans uint64
	for k := uint(0); k < 60; k++ {
		var x, y uint64
		for _, i := range a {
			if (uint64(i)>>k)&1 == 1 {
				x++
			} else {
				y++
			}
		}

		sum := (x * y) % mod
		for i := uint(0); i < k; i++ {
			sum = (sum * 2) % mod
		}

		ans = (ans + sum) % mod
	}

	fmt.Println(ans)
}

type Reader struct {
	rdr  *bufio.Reader
	size int
}

var reader *Reader

func NewReader(size int) {
	reader = &Reader{
		bufio.NewReaderSize(os.Stdin, size),
		size,
	}
}

func ReadLine() string {
	buf := make([]byte, 0, reader.size)
	for {
		line, isPrefix, err := reader.rdr.ReadLine()
		if err != nil {
			panic(err)
		}
		buf = append(buf, line...)
		if !isPrefix {
			break
		}
	}
	return string(buf)
}

func ReadStrs(sep string) []string {
	return strings.Split(ReadLine(), sep)
}

func ReadInts64(sep string) []int64 {
	a := ReadStrs(sep)
	n := make([]int64, 0)
	for _, v := range a {
		if i, e := strconv.ParseInt(v, 10, 64); e == nil {
			n = append(n, i)
		}
	}
	return n
}