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 9.2.1) (judge verdict: Accepted)

#include <iostream>
#include <cstdio>
#include <algorithm>
using namespace std;
const int mod = 1000000007;
const int MAXN = 300005;
long long bit[64]={0};
long long pow1[64]={0};
long long a[MAXN];
int maxlen = 0 ;
void add(long long a){
    int i;
    for(i=0;a;i++){
        bit[i]+=(a%2);
        a/=2;
    }
    maxlen = max(maxlen,i);
}
int main()
{
    pow1[0]=1;
    for(int i=1;i<63;i++)
        pow1[i]=pow1[i-1]*2%mod;
    int n;
    cin >> n;
    for(int i=0;i<n;i++){
        cin >> a[i];
        add(a[i]);
    }
    long long ans = 0 ;
    for(int j=0;j<n;j++){
        for(int i=0;i<maxlen;i++){
        if(a[j]&1)
            ans= (ans + pow1[i]*(n-bit[i])%mod)%mod;
        else
            ans= (ans + pow1[i]*bit[i]%mod)%mod;
            a[j]/=2;
        //cout << ans <<endl;
        }
    }
    cout << ans*((mod+1)/2)%mod << endl;
    return 0;
}