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 rep(i,n) for(int i=0; i<(n) ;i++)
#define pb push_back
#define all(v) (v).begin(),(v).end()
#define fi first
#define se second
#define sz(x) ((int)(x).size())
using ll=long long;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
#define MOD  1000000007
const ll INF=1e18;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b){ a = b; return 1; } return 0; }



int main(int argc, char const *argv[]) {
  int n;
  cin >> n;
  vector<ll> a(n);
  rep(i,n) cin >> a[i];

  ll ans=0;
  for(int bit=0; bit<60; bit++){
    int ones=0;//立っているビットの数
    rep(i,n){
      if(a[i]&1ll<<bit) ones++;
    }
  ans = (ll(ans) + (1ll << bit) % MOD * ones % MOD * (n-ones)) % MOD;
  }
  cout << ans << endl;
  return 0;
}