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: Time Limit Exceeded)

def main():
    n = int(input())
    a = [int(i) for i in input().split()]
    k = max(a).bit_length()
    mod = 10**9 + 7
    bk = [[0] * n for _ in range(k)]
    for kk in range(k):
        for i in range(n):
            bk[kk][i] = a[i] // 2**kk % 2
    bc = [[bk[kk][-1]] * n for kk in range(k)]
    for kk in range(k):
        for i in range(n - 1, 0, -1):
            bc[kk][i - 1] = bc[kk][i] + bk[kk][i - 1]
    c = 0
    for kk in range(k):
        kc = 0
        for i in range(n - 1):
            if bk[kk][i] == 0:
                kc = (kc + bc[kk][i + 1]) % mod
            else:
                kc = (kc + n - 1 - i - bc[kk][i + 1]) % mod
        kc = kc * pow(2, kk, mod) % mod
        c = (c + kc) % mod
    print(c)

if __name__ == '__main__':
    main()