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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define forloop(n) for(int i = 0; i < n; i++)
#define ll long long

#define mod 998244353

int main(){
	ios_base::sync_with_stdio(false); cin.tie(NULL);
	int n; cin>>n;
	vector<ll> vec(n);
	ll maks = 0;
	for(int i = 0; i < n; i++){
		cin>>vec[i];
		maks = max(maks, vec[i]);
	}
	sort(vec.rbegin(), vec.rend());
	ll res = 0, i = 0;
	while(vec[0] > 0){
		ll sifir = 0, bir = 0;
		for(int i = 0; i < n; i++){
			if(vec[i]%2) bir++;
			else sifir++;
			vec[i] /= 2;
		}
		ll v = 1;
		for(int u = 0; u < i; u++){
			v = (v*2)%1000000007;
		}
		res = (res + (bir * sifir)*v)%1000000007;
		i++;
	}
	cout<<res;
	return 0; 
}