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)

def read():
    N = int(input().strip())
    A = list(map(int, input().strip().split()))
    return N, A

def digits2int(c, L, MOD):
    
    return base


def solve(N, A, L=60, MOD=10**9+7):
    # j桁目のビットが1であるものの数を、累積和として記憶
    count_ones = [[0 for j in range(L+1)] for i in range(N+1)]
    for i in range(N):
        for j in range(L):
            count_ones[i+1][j] = count_ones[i][j] + ((A[i] >> j) & 1)
    # A[i] と A[j] (i<j) のxorをとる
    modsum = 0
    for i in range(N-1):
        c = [0 for j in range(L)]
        for j in range(L):
            if ((A[i] >> j) & 1) == 0:
                c[j] = count_ones[N][j] - count_ones[i+1][j]
            else:
                c[j] = (N-i-1) - (count_ones[N][j] - count_ones[i+1][j])
        # digit2int
        for i in range(L):
            if c[i] > 0:
                f = (c[i] << i) % MOD
                modsum = (modsum + f) % MOD
    return modsum


if __name__ == '__main__':
    inputs = read()
    print("%d" % solve(*inputs))