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 PHP7 (7.0.15) (judge verdict: Time Limit Exceeded)

<?php
define('MOD', pow(10, 9) + 7);
define('BIT', 60);
$x[0] = 1;
for ($i = 1; $i < BIT; $i++) {
    $x[$i] = $x[$i - 1] * 2;
    $x[$i] %= MOD;
}

fscanf(STDIN, "%d", $N);
$a = array_map('intval', explode(' ', trim(fgets(STDIN))));

$k[0] = array_pad(array(), BIT, 0);
$k[1] = array_pad(array(), BIT, 0);
$ans = 0;
for ($i = 0; $i < $N; $i++) {
    //$s = array_map('intval', array_reverse(str_split(base_convert($a[$i], 10, 2))));
    $s = array_map('intval', array_reverse(str_split(str_pad(decbin($a[$i]), BIT, '0', STR_PAD_LEFT))));
    for ($j = 0; $j < BIT; $j++) {
        //$s[$j] = $s[$j] ?? 0;
        $ans += $k[1 - $s[$j]][$j] * $x[$j];
        $k[$s[$j]][$j]++;
    }
    $ans %= MOD;
}
printf("%d", $ans);