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 Fortran (gfortran v4.8.4) (judge verdict: Wrong Answer)

program xor_sum4
    implicit none
    integer(8),parameter:: md = 1000000007
    integer(4):: i,j,k
    integer(4):: n
    integer(8),allocatable::a(:), total_bits(:)
    integer(8):: ans=0
    
    read*, n
    allocate(a(n))
    allocate(total_bits(0:100), source=0_8)
    read*,a(:)

    do i=1,n
        do j=0,100
            if (btest(a(i),j)) total_bits(j) = total_bits(j) + 1
        end do
    end do
    
    do i=0,100
        ans = mod(ans + mod(mod(lshift(total_bits(i)*(n-total_bits(i)),i),md),md),md)
    end do

    print*, ans

end program xor_sum4