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 (1.42.0) (judge verdict: Accepted)

use std::io::Read;

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

    let answer = solve(&buf);

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

fn solve(input: &str) -> String {
    let mut iterator = input.split_whitespace();

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

    let k: usize = keta(*a.iter().max().unwrap());
    let mut v: Vec<Vec<usize>> = vec![vec![0, 0]; k];
    for i in 0..n {
        let mut ai = a[i];
        for j in (0..k).rev() {
            v[j][ai % 2] += 1;
            ai /= 2;
        }
    }

    const MOD: usize = 1_000_000_007;
    let mut ans: usize = 0;
    let mut x = 1;
    for i in (0..k).rev() {
        ans += (((v[i][0] * v[i][1]) % MOD) * x) % MOD;
        ans %= MOD;
        x = (x * 2) % MOD;
    }
    ans.to_string()
}

fn keta(mut x: usize) -> usize {
    if x == 0 {
        return 0;
    }
    let mut result = 0;
    while x > 0 {
        x /= 2;
        result += 1;
    }
    result
}