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: Accepted)

#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> P;
typedef pair<ll,ll> Pl;
#define all(a) (a).begin(),(a).end()
#define rep(i,n) repi(i,0,n)
#define repi(i,a,b) for(ll i=(a);i<(b);i++)
#define rrep(i,n) for(ll (i)=(n)-1;(i)>=0;i--)
#define SHOW(x) cout << #x << ": " << x << endl;
const ll INF=1e18,MOD = 1e9+7;
const int iINF = 1e9;
int main(){
    ll n,ans = 0;
    cin>>n;
    vector<ll>bitcnt(62,0);
    rep(i,n){
        ll a;
        cin>>a;
        rep(j,60){
            if(a & (1LL << j)){
                bitcnt[j]++;
            }
        }
    }
    rep(i,60){
        ll notbit = n - bitcnt[i];
        ll standbit =  notbit * bitcnt[i];
        ans += ((1LL << i)%MOD * (standbit%MOD))%MOD;
        ans %= MOD;
    }
    cout<<ans<<endl;
}