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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

N=int(input())
A=list(map(int,input().split()))
 
def jouyo(X):
    return X%1000000007
 
MAX=A[0]
for i in range(N):
    if MAX<=A[i]:
        MAX = A[i]
    else:
        MAX = MAX
 
p = 1
M = 1
for i in range(60):
    if 2*p <= MAX:
        p = 2*p
        M = M+1
    else:
        break
        
e=[]
for i in range(M+1):
  	e.append(2**i)
 
List = []        
for i in range(1,M+1):
    count = 0
    for j in range(N):
        if A[j]%e[i] >= e[i-1]:
            count = count +1
        else:
            count = count
    List.append(count)
    
ans = 0   
for i in range(M):
    ans = jouyo(ans) + jouyo(jouyo(e[i])*jouyo(jouyo(List[i])*jouyo(N-List[i])))
    
print(jouyo(ans))