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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayDeque;
import java.util.Deque;
import java.util.regex.Pattern;

public class Main {
    public void solve(Stdin stdin, PrintWriter stdout) throws NumberFormatException, IOException {
        int n = stdin.nextInt();
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = stdin.nextLong();
        }

        int[] c = new int[61];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < 61L; j++) {
                if ((a[i] & (1L << j)) != 0) {
                    c[j]++;
                }
            }
        }

        long ans = 0;
        long d = 1;
        for (int i = 0; i < 61; i++) {
            ans += mul(mul(c[i], n - c[i]), d);
            ans %= mod;
            d *= 2L;
        }
        stdout.println(ans);
    }

    private long mul(long x, long y) {
        return (x * y) % 1000000007L;
    }

    private long mod = 1000000007L;

    public static void main(String[] args) throws NumberFormatException, IOException {
        Stdin stdin = new Stdin();
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().solve(stdin, stdout);
        stdout.flush();
    }

    public static class Stdin {
        private Deque<String> queue;
        private BufferedReader stdin;
        private Pattern delimiter;

        public Stdin() {
            queue = new ArrayDeque<>();
            stdin = new BufferedReader(new InputStreamReader(System.in));
            delimiter = Pattern.compile(" ");
        }

        public String next() throws IOException {
            if (queue.isEmpty()) {
                delimiter.splitAsStream(stdin.readLine()).forEach(queue::addLast);
            }
            return queue.removeFirst();
        }

        public int nextInt() throws NumberFormatException, IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws NumberFormatException, IOException {
            return Long.parseLong(next());
        }
    }
}