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::cmp::{max, min};
use std::collections::VecDeque;
use std::io::{stdin, Read};
use std::str::FromStr;

// https://qiita.com/tubo28/items/e6076e9040da57368845
fn read<T: FromStr>() -> T {
    let stdin = stdin();
    let stdin = stdin.lock();
    let token: String = stdin
        .bytes()
        .map(|c| c.expect("failed to read char") as char)
        .skip_while(|c| c.is_whitespace())
        .take_while(|c| !c.is_whitespace())
        .collect();
    token.parse().ok().expect("failed to parse token")
}

#[allow(dead_code)]
fn main() {
    let n = read::<usize>();
    let a = (0..n).map(|_| read::<usize>()).collect::<Vec<_>>();
    let msb = 60;
    let mut t = vec![vec![0; msb + 1]; n + 1];

    for s in 0..msb {
        t[0][s] = if (a[0] & (1 << s)) > 0 { 1 } else { 0 };
    }

    for i in 1..n {
        for s in 0..msb {
            t[i][s] = t[i - 1][s] + (if a[i] & (1 << s) > 0 { 1 } else { 0 })
        }
    }

    let mut ans = 0;

    for i in 0..(n - 1) {
        for s in 0..msb {
            let stand = t[n - 1][s] - t[i][s];
            if a[i] & (1 << s) == 0 {
                ans += (((1 << s) % 1000000007) * stand % 1000000007);
                ans %= 1000000007
            } else {
                let no_stand = (n - (i + 1)) - stand;
                ans += (((1 << s) % 1000000007) * no_stand % 1000000007);
                ans %= 1000000007
            }
        }
    }
    println!("{}", ans)
}