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)

#pragma GCC optimize("Ofast")
#include<bits/stdc++.h>
using namespace std;
struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);}} __init;
#define max3(a,b,c) max(a,max(b,c))
#define min3(a,b,c) min(a,min(b,c))
#define MOD 1000000007
#define INF (1<<30)
#define LINF (lint)(1LL<<56)
#define endl "\n"
#define rep(i,n) for(int (i)=0;(i)<(n);(i)++)
#define reprev(i,n) for(int (i)=(n-1);(i)>=0;(i)--)
#define Flag(x) (1<<(x))
#define Flagcount(x) __builtin_popcount(x)
#define pint pair<int,int>
#define pdouble pair<double,double>
#define plint pair<lint,lint>
typedef unsigned long long int ull;
typedef long long lint;

long long powmod(lint a,lint b){
  return b?powmod(a*a%MOD,b/2)*(b%2?a:1)%MOD:1;
}

int main(void){
    lint N;
    lint div2=powmod(2,MOD-2);
    cin >> N;
    lint A[N];
    lint Amod[N];
    rep(i,N){
        cin >> A[i];
        Amod[i]=A[i]%MOD;
    }
    lint ans=0;
    lint sum=0;
    lint minus=0;
    rep(i,N) sum=(sum+Amod[i]*(N-1))%MOD;
    lint bitcount[60]={};
    rep(i,N){
        rep(j,60) if(A[i]&1LL<<j) bitcount[j]++;
    }
    rep(i,60){
        lint bito=(1LL<<i)%MOD;
        minus=(minus+((bito*((bitcount[i]*(bitcount[i]-1))%MOD))%MOD))%MOD;
    }
    sum-=minus;
    if(sum<0) sum+=MOD;
    cout << sum << endl;
}