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;

# define C continue;
# define R return

# define D double
# define I insert
# define ll long long
# define ld long double

# define ull unsigned long long
# define ui unsigned int

# define pb push_back
# define pf push_front

# define vi vector < ll >
# define vc vector < char >
# define vs vector < string >
# define vb vector < bool >
# define vd vector < D >
# define vll vector < ll >
# define vull vector < ull >
# define vld vector < ld >

# define vvi vector < vector < ll > >
# define vvb vector < vector < bool > >
# define vvc vector < vector < char > >
# define vvll vector < vector < ll > >
# define vvd vector < vector < D > >
# define vvld vector < vector < ld > >

# define all(v) (v).begin() , (v).end()
# define allrev(v) (v).rbegin() , (v).rend()
# define allcomp(v) v.begin() , v.end() , comp
# define allrevcomp(v) v.rbegin() , v.rend() , comp

# define pii pair < ll , ll >
# define pll pair < ll , ll >
# define pld pair < ld , ld >
# define pDD pair < D , D >

# define vpld vector < pld >
# define vpii vector < pii >
# define vpll vector < pll >
# define vpDD vector < pDD >

# define vvpii vector < vector < pii > >
# define F first
# define S second
# define mp make_pair

# define dist(a,b,p,q) sqrt((p-a)*(p-a) + (q-b)*(q-b))

# define pp(n) printf("%.10Lf",n);
# define line cout<<"\n";
# define fast ios_base::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0);

string vow = "aeiou";

const ll dxhorse[] = {-2, -2, -1, -1, 1, 1, 2, 2};
const ll dyhorse[] = {1, -1, 2, -2, 2, -2, 1, -1};

const ll dx[] = { -1 , 0 , 0 , 1 } ;
const ll dy[] = { 0 , -1 , 1 , 0 } ;

const ld pie = 3.14159265358979 ;
const ll mod = 1e9 + 7 ;

void solve ( ll test_case )
{
    ll n ; cin >> n ;
    vi bit ( 62 ) ;

    for ( ll i=0 ; i < n ; i ++ )
    {
        ll val ; cin >> val ;

        for ( ll j = 0 ; j < 62 ; j++ )
        {
            ll temp = (val&1) ;
            val >>= 1 ;

            if ( temp )
                bit[j] ++ ;
        }
    }

    ll f = 1 ;
    ll ans = 0 ;

    for ( ll j = 0 ; j < 62 ; j ++ )
    {
        ll one = bit[j] ;
        ll zero = n - one ;

        ll temp = one * f ;
        temp %= mod ;

        temp *= zero ;
        temp %= mod ;

        ans += temp ;
        ans %= mod ;

        f <<= 1 ;
        f %= mod ;
    }

    cout << ans ; line
}

int main()
{
    ll t = 1;
    // cin >> t;

    for ( ll i=0 ; i < t ; i++ ) solve(i);
    return 0;
}