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
fscanf(STDIN, "%d", $in_n);
$in_a_str = trim(fgets(STDIN));

$arr_in_a_str = explode(" ", $in_a_str, $in_n);

for($i = 0; $i < $in_n; $i++) {
    $arr_in_a[$i] = intval($arr_in_a_str[$i]);
}

//var_dump($arr_in_a);
//var_dump(PHP_INT_MAX);
//var_dump(2**60);

$waru = (10 ** 9) + 7;
$ans = 0;

for($i = 0; $i < $in_n - 1; $i++){
    for($j = $i + 1; $j < $in_n; $j++) {
//        echo "$i , $j : ";
//        var_dump($arr_in_a[$i] ^ $arr_in_a[$j] );
        $ans += ($arr_in_a[$i] ^ $arr_in_a[$j]) % $waru;
//        $ans += ($arr_in_a[$i] ^ $arr_in_a[$j]);
    }
    if ($ans > $waru) {
        $ans = $ans % $waru;
    }
}

echo "$ans\n";

?>