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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::prelude::*;

fn main() {
    let mut input_str = String::new();
    std::io::stdin().read_to_string(&mut input_str).unwrap();

    let input_parts = input_str.split_whitespace().collect::<Vec<_>>();
    let mut input_parts_it = input_parts.iter().cloned();
    let mut next = || input_parts_it.next().unwrap();

    let n: usize = next().parse().unwrap();
    let a: Vec<u64> = (0..n).map(|_| next().parse().unwrap()).collect();

    let mut a_sum = vec![0; a.len() + 1];

    let sum = (0..60u32)
        .map(|bit| {
            for i in 1..a.len() + 1 {
                a_sum[i] = a_sum[i - 1] + ((a[i - 1] >> bit) & 1);
            }

            let sum: u64 = (0..a.len() - 1)
                .map(|i| {
                    let j = i + 1..a.len();
                    let set_count = a_sum[j.end] - a_sum[j.start];
                    if (a[i] >> bit) & 1 != 0 {
                        (j.end - j.start) as u64 - set_count
                    } else {
                        set_count
                    }
                })
                .sum();

            (0..bit).fold(sum, |x, _| (x * 2) % 1000000007)
        })
        .fold(0, |x, y| (x + y) % 1000000007);

    println!("{}", sum);
}