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: Wrong Answer)

package main

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

const MOD = 1e9 + 7

func main() {
	sc := bufio.NewScanner(os.Stdin)
	//ns := sc.Text()
	sc.Scan()
	sc.Scan()
	as := sc.Text()

	//N, _ := strconv.Atoi(ns)
	A := make([]int, 60)
	AZ := make([]int, 60)
	for _, as := range strings.Split(as, " ") {
		a, _ := strconv.Atoi(as)
		for i := 0; i < 60; i++ {
			if a&(1<<uint(i)) == 0 {
				AZ[i] += 1
			} else {
				A[i] += 1
			}
		}
	}

	sum := 0
	for i := 0; i < 60; i++ {
		p := ModPow(2, i)
		sum = (sum + ModMul(ModMul(AZ[i], A[i]), p)) % MOD
	}
	fmt.Println(sum)
}

func ModPow(a, n int) int {
	var r int = 1
	for n > 0 {
		if n&1 == 1 {
			r = r * a % MOD
		}
		a = a * a % MOD
		n >>= 1
	}
	return r
}

func ModMul(a, b int) int {
	return a * b % MOD
}