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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define REP(i, e) for(int (i) = 0; (i) < (e); ++(i))
#define FOR(i, b, e) for(int (i) = (b); (i) < (e); ++(i))
#define ALL(c) (c).begin(), (c).end()
#define PRINT(x) cout << (x) << "\n"
using namespace std;
using ll = long long; using pint = pair<int, int>; using pll = pair<ll, ll>;
template<typename T> auto compare = [](T x, T y) -> bool{return (x < y);};
const int MOD = 1000000007;

ll N;
map<ll, ll> mp;
ll pow2[61];

signed main(){
    cin >> N;
    unsigned long long a;
    REP(i, N){
        cin >> a;
        REP(j, 61){
            if(a == 0) continue;
            if(a % 2 == 1) mp[j]++;
            a /= 2;
        }
    }
    pow2[0] = 1;
    REP(i, 60) pow2[i + 1] = (pow2[i] * 2) % MOD;
    ll ans = 0;
    REP(i, 61){
        ll k = mp[i] * (N - mp[i]) % MOD;
        ans = (ans + k * pow2[i] % MOD) % MOD;
    }
    PRINT(ans);
    return 0;
}