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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.BufferedInputStream;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author MaxHeap
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        DXorSum4 solver = new DXorSum4();
        solver.solve(1, in, out);
        out.close();
    }

    static class DXorSum4 {
        private static final long MOD = (long) (1e9 + 7);

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            long[] arr = new long[n];
            for (int i = 0; i < n; ++i) {
                arr[i] = in.nextLong();
            }
            long sum = 0;
            for (int i = 0; i < 62; i++) {
                long zeroCount = 0, oneCount = 0, bitSum = 0;
                for (int j = 0; j < n; j++) {
                    if ((arr[j] & 1) == 0) {
                        zeroCount++;
                    } else {
                        oneCount++;
                    }
                }
                bitSum = oneCount * zeroCount;
                bitSum = ((bitSum % MOD) * (1L << i)) % MOD;
                sum = (sum + bitSum) % MOD;
                for (int j = 0; j < n; ++j) {
                    arr[j] >>= 1L;
                }
            }
            out.println(sum);
        }

    }

    static class InputReader {
        private StringTokenizer st;
        private BufferedReader reader;

        public InputReader(InputStream is) {
            st = null;
            reader = new BufferedReader(new InputStreamReader(new BufferedInputStream(is, 1 << 18)));
        }

        public String next() {
            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    return null;
                }
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

    }
}