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Contest: Task: Related: TaskC TaskE

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 $(10^9+7)$.