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: Time Limit Exceeded)

import java.util.*;
import java.io.*;
public class Main {
    static long mod = 1000000007;
    static ArrayList<Long> A = new ArrayList<Long>();
    public static void main(String[] args) throws Exception {
        InputStreamReader r = new InputStreamReader(System.in);
        int N = nextInt(r);
        A.add(nextLong(r));
        long ans = 0;
        for (int i = 1; i < N; i++) {
            long n = nextLong(r);
            ans += xorSum(n) % mod;
            A.add(n);
        }
        System.out.println(ans % mod);
    }

    public static int nextInt(InputStreamReader r) throws Exception {
        String str = "";
        while (true) {
            int c = r.read();
            if (c == 32 || c == 10 || c == -1) {
                break;
            }
            str += (char)c;
        }
        return Integer.parseInt(str);
    }

    public static long nextLong(InputStreamReader r) throws Exception {
        String str = "";
        while (true) {
            int c = r.read();
            if (c == 32 || c == 10 || c == -1) {
                break;
            }
            str += (char)c;
        }
        return Long.parseLong(str);
    }

    public static long xorSum(long n) {
        long res = 0;
        int[] now = set(n);
        for (long x : A) {
            int[] xor = set(x);
            res += sum(now, xor);
        }
        return res % mod;
    }

    public static int[] set(long n) {
        int[] res = new int[60];
        for (int i = 0; i < 60; i++) {
            res[i] = n % 2 == 1 ? 1 : 0;
            n = n / 2;
            if (n == 0) break;
        }
        return res;
    }

    public static long sum(int[] now, int[] xor) {
        long res = 0;
        for (int i = 0; i < 60; i++) {
            if (now[i] != xor[i]) {
                res += pow(i) % mod;
            }
        }
        return res % mod;
    }

    public static long pow(int i) {
        return i == 0 ? 1 : 2 * pow(i-1);
    }
}