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 PyPy3 (2.4.0) (judge verdict: Accepted)

n = int(input())
A = list(map(int,input().split()))
MOD = 10**9 + 7
for i in range(n):
  b = format(A[i],'b').zfill(61)
  A[i] = b


bit = [0]*61
for i in range(n):
  for j in range(61):
    if A[i][j] =='1':
      bit[j] += 1

ans = 0
for k in range(61):
  multi = (bit[k]*(n-bit[k]))%MOD
  if k > 30:
    ans += (((2**(60-k))%MOD) * multi)%MOD
  else:
    ooo = ((2**(30-k))%MOD * (2**20)%MOD * (2**10)%MOD) %MOD
    ans += (ooo * multi)%MOD
  ans %= MOD
print(ans)