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>
#define rep(i,a,b) for(ll i=ll(a);i<ll(b);i++)
#define irep(i,a,b) for(ll i=ll(a);i>=ll(b);i--)
#define pb push_back
#define mp make_pair
#define pll pair<ll,ll>
#define F .first
#define S .second 
using ll=long long;
using ld=long double;
using namespace std;
const ll mod=1e9+7;
ll a[330000];
main(){
  ll n,ans=0,tmp,tmp2;
  cin>>n;
  rep(i,0,n)cin>>a[i];
  rep(i,0,61){
    tmp=0,tmp2=0;
    ll f=powl((ll)2,i);
    f%=mod;
    rep(j,0,n){
      if((a[j]>>i)&1)tmp++;
    }
    tmp=(tmp*(n-tmp))%mod;
    ans=(ans+f*tmp)%mod;
  }
  cout<<ans%mod;
}