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 (
	"fmt"
	"bufio"
	"os"
	"strconv"
)

var (
	sc = bufio.NewScanner(os.Stdin)
	wtr = bufio.NewWriter(os.Stdout)
)

func scanInt() int {
	sc.Scan()
	a,_ := strconv.Atoi(sc.Text())
	return a
}

func scanText() string {
	sc.Scan()
	return sc.Text()
}

func main() {
	sc.Split(bufio.ScanWords)

	n := scanInt()
	a := make([]uint, n)

	for i := 0; i < n; i++ {
		a[i] = uint(scanInt())
	}

	cnt := make([]uint, 61)
	for _,ai:=range a{
		for i:=uint(0);i<=60;i++{
			cnt[i] +=(uint(ai) >> i)&1
		}
	}
 
	ans :=uint(0)
	for i, v:=range cnt{
		ans = (ans + ((v*(uint(n)-v))%mod * ((1<<uint(i)) % mod))) %mod
	}

	fmt.Println(ans)
}

const mod = 1000000007