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 C (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>
#include<ctype.h>
#include<string.h>
#include<assert.h>

typedef long long ull;
typedef unsigned long long ll;

#define mod 1000000007LL

int main()
{
    int n;
    ll* a;
    ll sum = 0, b, m;
    scanf("%d", &n);
    a = calloc(n, sizeof(ll));
    for (size_t i = 0; i < n; i++)
    {
        scanf("%lld", a + i);
    }

    b = 1;
    for (size_t i = 0; i < 61; i++)
    {
        m = 0;
        for (size_t j = 0; j < n; j++)
        {
            m += !!(a[j] & b);
        }
        sum += ((((b % mod) * (n - m)) % mod) * m) % mod;
        sum %= mod;
        b <<= 1;
    }

    printf("%lld", sum);

    return 0;
}