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: Wrong Answer)

n = int(input())
a = [int(_) for _ in input().split()]
M = max(a)
p = len(format(M, 'b'))
l = [[0 for _ in range(n)] for _ in range(p)]
for i in range(n):
    a_s = format(a[i], '0' + str(p) + 'b')
    for c in range(p):
        l[c][i] = int(a_s[c])
# for i in range(p):
#     print(l[i])
s = [[0 for _ in range(n+1)] for _ in range(p)]
for i in range(p):
    for j in range(n):
        s[i][j+1] = s[i][j] + l[i][j]
# for i in range(p):
#     print(s[i])
ans = 0
for j in range(n-1):
    for i in range(p):
        if l[i][j] == 1:
            ans += ((2**(p - i - 1)) * (n - j - 1) - (s[i][n] - s[i][j+1]))
        else:
            ans += (2**(p - i - 1)) * (s[i][n] - s[i][j+1])
        ans = ans % ((10**9) + 7)
print(ans)