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 Perl (v5.18.2) (judge verdict: Time Limit Exceeded)

use v5.18; # strict say state
use warnings;
use Memoize;

chomp (my $n = <STDIN>);
chomp (my @a = split / /, <STDIN>);
my (@b, @c);
for my $i (0..($n-1)) {
  $b = $a[$i];
  my $j = 0;
  while ($b) {
    $c[$j] += $b % 2;
    $b >>= 1;
    $j++;
  }
}
my $MOD = 1e9 + 7;
sub modpow {
  my ($a, $n) = @_;
  my $r = 1;
  my $MOD = 1e9 + 7;
  while ($n > 0) {
    $r = $r * $a % $MOD if $n & 1;
    $a = $a * $a % $MOD;
    $n >>= 1;
  }
  return $r;
}
memoize('modpow');
my @in;
for my $i (0..60) {
  $in[$i] = modpow(2, $i);
}
my $ans = 0;
for my $i (0..@c-1) {
  my $b = $in[$i];
  $b *= $c[$i];
  $b %= $MOD;
  $b *= $n - $c[$i];
  $b %= $MOD;
  $ans += $b;
  $ans %= $MOD;
}
say $ans;