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)

#!/usr/bin/env python3
import sys

MOD = 1000000007  # type: int


def solve(N: int, A: "List[int]"):
    a_sum = [int()]*60

    for a in A:
        for i, r_a in enumerate(format(a, "b")[::-1]):
            if r_a == "1":
                a_sum[i] += 1

    a_sum = [a_s_*(2**i)%MOD for i, a_s_ in zip(range(60), a_sum)]
    a_acc_sum = [_ for _ in a_sum]
    for x in range(1,60):
        a_acc_sum[x] = a_acc_sum[x-1] + a_acc_sum[x] 
    
    ans = 0
    for a in A:
        for i, r_a in enumerate(format(a, "b")[::-1]):
            if r_a == "0":
                ans += a_sum[i]
        
        ans += a_acc_sum[59] - a_acc_sum[i]

        # for ic in range(i+1,60):
            # ans+=a_sum[ic]
            # ans%=MOD

    print(ans%MOD)

    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    A = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    solve(N, A)

if __name__ == '__main__':
    main()