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::vec::Vec;

fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

const MOD: usize = 1_000_000_000 + 7;
fn main() {
    let n: usize = read();
    let a: Vec<usize> = read_vec();
    let l = 61;
    let mut table = vec![vec![0; l]; n+1];

    // 各桁に立っているビットを数える
    for i in (0..n).rev() {
      for j in 0..l {
        table[i][j] = table[i+1][j];
        let flag: usize = 1<<j;
        if (flag & a[i]) == flag {
           table[i][j] += 1;
        }
      }
    }

    let mut ans: usize = 0;

    for i in 1..n {
      for j in 0..l {
        let tmp: usize = n - i;
        //println!("{} {} {:?} {} ", ans, a[i-1], table[i], tmp);
        let flag: usize = 1<<j;
  
        if table[i][j] == 0 && (a[i-1] & flag) == flag {
           ans += tmp * (flag % MOD);
           ans %= MOD;
        } else if table[i][j] < tmp && (a[i-1] & flag) == flag {
          ans += (tmp - table[i][j]) * (flag % MOD);
          ans %= MOD
        } else if table[i][j] > 0 && (a[i-1] & flag) != flag {
          ans += table[i][j] * (flag % MOD);
          ans %= MOD;
        }
      }
    }
    println!("{}", ans);

    // for x in table {
    //   println!("{:?}", x);
    // }
}