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>
typedef long long ll;
using namespace std;
#define repr(i,a,b) for(int i=a;i<b;i++)
#define rep(i,n) for(int i=0;i<n;i++)
#define invrepr(i,a,b) for(int i=b-1;i>=a;i--)
#define invrep(i,n) invrepr(i,0,n)
#define repitr(itr,a) for(auto itr=a.begin();itr!=a.end();++itr)
#define P pair<int,int>
const int MOD=1e9+7;
const int INF=2e9;


int main() {
    ios_base::sync_with_stdio(false); 

    int n;
    cin >> n;
    vector<ll> cnt(65);
    rep(i,n) {
        ll a;
        cin >> a;
        ll ele=1;
        int c=0;
        while (a>0) {
            ele*=2;
            if (a%ele>0) ++cnt[c];
            a=a-a%ele;
            ++c;
        }
    }
    ll ele=1,ans=0;
    rep(i,61) {
        ans+=(ele*(cnt[i]*(n-cnt[i]))%MOD)%MOD;
        ans=ans%MOD;
        ele*=2;
    }
    cout << ans << endl;

    return 0;
}