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: Accepted)

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

public class Main {

    static long MOD = 1_000_000_000 + 7;

    public static void main(String[] args) throws Exception {
        long startTime = System.nanoTime();
        int t = 1;
        while (t-- > 0) {
            solve();
        }
        long endTime = System.nanoTime();
        err.println("Execution Time : +" + (endTime - startTime) / 1000000 + " ms");
        exit(0);
    }

    static void solve() {
        int n = in.nextInt();
        long[] data = in.readAllLongs(n);
        int[][] sum = new int[n][70];
        long[] pow_2 = new long[70];
        for (int i = 0; i < 70; i++) {
            pow_2[i] = mod_pow(2, i);
        }
        long ans = 0;
        for (int i = n - 1, l = 0; i >= 0; i--, l++) {
            int[] d = getInts(data[i]);
            for (int j = d.length - 1, k = 0; j >= 0; j--, k++) {
                if (l > 0) {
                    int p = l - sum[i + 1][j];
                    if (d[j] == 1) {
                        ans += pow_2[k] * p;
                    } else {
                        ans += pow_2[k] * sum[i + 1][j];
                    }
                }
                ans %= MOD;
                sum[i][j] += d[j];
                if (i + 1 < n) {
                    sum[i][j] += sum[i + 1][j];
                }
            }
        }
        out.println(ans);
    }

    private static int[] getInts(long datum) {
        int[] temp = new int[64];
        int len = 63;
        while (datum > 0) {
            temp[len--] = (int) (datum % 2);
            datum /= 2;
        }
        return temp;
    }

    static String app(String v) {
        int target = 64 - v.length();
        StringBuilder p = new StringBuilder();
        for (int i = 0; i < target; i++) {
            p.append(0);
        }
        p.append(v);
        return p.toString();
    }

    static long mod_pow(long x, long y) {
        if (y == 0) {
            return 1;
        }
        if (y == 1) {
            return x;
        }
        long v = mod_pow(x, y / 2);
        if ((y & 1) > 0) {
            return v * v % MOD * x % MOD;
        }
        return v * v % MOD;
    }

    static long compute(int ind) {
        return mod_pow(2, ind);
    }

    static void debug(Object... args) {
        for (Object a : args) {
            out.println(a);
        }
    }

    static void y() {
        out.println("YES");
    }

    static void n() {
        out.println("NO");
    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

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

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

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

        public int[] readAllInts(int n) {
            int[] p = new int[n];
            for (int i = 0; i < n; i++) {
                p[i] = in.nextInt();
            }
            return p;
        }

        public int[] readAllInts(int n, int s) {
            int[] p = new int[n + s];
            for (int i = s; i < n + s; i++) {
                p[i] = in.nextInt();
            }
            return p;
        }

        public long[] readAllLongs(int n) {
            long[] p = new long[n];
            for (int i = 0; i < n; i++) {
                p[i] = in.nextLong();
            }
            return p;
        }

        public long[] readAllLongs(int n, int s) {
            long[] p = new long[n + s];
            for (int i = s; i < n + s; i++) {
                p[i] = in.nextInt();
            }
            return p;
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }
    }

    static void exit(int a) {
        out.close();
        err.close();
        System.exit(a);
    }

    static InputStream inputStream = System.in;
    static OutputStream outputStream = System.out;
    static OutputStream errStream = System.err;
    static InputReader in = new InputReader(inputStream);
    static PrintWriter out = new PrintWriter(outputStream);
    static PrintWriter err = new PrintWriter(errStream);
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

}