101473: [AtCoder]ABC147 D - Xor Sum 4
Memory Limit：256 MB
Time Limit：2 S
Judge Style：Text Compare
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Solved：0
Description
Score : $400$ points
Problem Statement
We have $N$ integers. The $i$-th integer is $A_i$.
Find $\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \text{ XOR } A_j)$, modulo $(10^9+7)$.
What is $\text{ XOR }$?
The XOR of integers $A$ and $B$, $A \text{ XOR } B$, is defined as follows:
- When $A \text{ XOR } B$ 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.
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 $\sum_{i=1}^{N-1}\sum_{j=i+1}^{N} (A_i \text{ XOR } A_j)$, modulo $(10^9+7)$.
Sample Input 1
3 1 2 3
Sample Output 1
6
We have $(1\text{ XOR } 2)+(1\text{ XOR } 3)+(2\text{ XOR } 3)=3+2+1=6$.
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 $(10^9+7)$.