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)

import sys
def input(): return sys.stdin.readline().strip()
def INT(): return int(input())
def LIST(): return list(map(int, input().split()))
mod = 10 ** 9 + 7

#0埋め　桁合わせ
def digit(n, r):
    n = str(n)
    l = len(n)
    n = '0' * (r - l) + n
    return n

n = INT()
a = LIST()
arr = [0 for _ in range(61)]
arr2 = [0 for _ in range(61)]
for i in range(1, n + 1):
    bn = bin(a[i - 1])[2:]
    for j in range(len(bn)):
        arr[j + 61 - len(bn)] += int(bn[j])
for i in range(61):
    arr2[i] = n - arr[i]
    if arr2[i] == n:
        arr2[i] = 0
ans = 0
for i in range(61):
    ans *= 2
    ans += arr[i] * arr2[i]
    ans %= mod
print(ans)