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: Wrong Answer)

const MOD_N: u64 = 1000000007;

fn bit_cnt_add(bit_cnt: &mut Vec<Vec<u32>>, x: u64) {
    for i in 0..64 {
        let bit_x = ((x >> i) & 1) as usize;
        bit_cnt[i][bit_x] += 1;
    }
}

fn xor_add_bits(bit_cnt: &Vec<Vec<u32>>, xor_x: u64) -> u64 {
    let mut result = 0u64;
    let mut carry = 0u64;

    for i in 0..64 {
        let bit_x = if ((xor_x >> i) & 1) == 0 { 1usize } else { 0usize };

        let nr_one = (bit_cnt[i][bit_x] as u64) + carry;

        carry = nr_one/2;
        let set_bit = nr_one%2;

        result |= set_bit << i;
    }

    result % MOD_N
}

fn main() {
    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let mut iter = buf.split_whitespace();
    let n: usize = iter.next().unwrap().parse().unwrap();

    let mut buf = String::new();
    std::io::stdin().read_line(&mut buf).unwrap();
    let a_s = buf.split_whitespace()
        .map(|x| x.parse::<u64>().unwrap())
        .collect::<Vec<_>>();

    let mut bit_cnt = vec![vec![0u32; 2]; 64];

    let mut ans = 0u64;

    for i in (1..n).rev() {
        bit_cnt_add(&mut bit_cnt, a_s[i]);
        ans += xor_add_bits(&bit_cnt, a_s[i-1]);
        ans %= MOD_N;
    }

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