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)

#![allow(unused_imports)]

use proconio::{input, fastout};
use proconio::marker::*;
use rand::random;

const MOD: usize = 1_000_000_007;

#[fastout]
fn main() {
    input! {
    n: usize,
    a: [usize; n]
    }
    let mut a_max = *(a.iter().max().unwrap());
    let mut k = 0;
    while a_max > 0 {
        a_max /= 2;
        k += 1;
    }
    let mut ans = 0;
    for i in 0..k {
        let (mut p, mut q) = (0, 0);
        for j in 0..n {
            if a[j] & 1 << i > 0 {
                p += 1;
            } else {
                q += 1;
            }
        }
        ans += (p * q) % MOD * (2usize.pow(i as u32) % MOD);
        ans %= MOD;
    }
    println!("{}", ans);
}