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)

import sys
import numpy as np

MOD = 10 ** 9 + 7

n, *a = map(int, sys.stdin.read().split())
a = np.array(a, dtype=np.int64)

powmod = [None] * 61
powmod[0] = 1
for i in range(60):
    powmod[i+1] = powmod[i] * 2 % MOD
powmod = np.array(powmod, dtype=np.int64)

def main():
    b = a >> np.arange(61).reshape(-1, 1) & 1
    x = np.count_nonzero(b, axis=1)
    y = n - x
    x *= y 
    x %= MOD
    x *= powmod
    x %= MOD
    
    ans = np.sum(x) % MOD
    return ans

if __name__ == '__main__':
    ans = main()
    print(ans)