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: Wrong Answer)

#define _USE_MATH_DEFINES
#include<iostream>
#include<fstream>
#include<string>
#include<vector>
#include<utility>
#include<algorithm>
#include<climits>
#include<set>
#include<map>
#include<cmath>
#include<iomanip>
#include<iterator>
#include<queue>
#include<stack>
#include<cctype>
#include<deque>
#include<time.h>
#include<bitset>
#include<random>
#include<unordered_set>
#include<unordered_map>
#include<sstream>
#include<random>

//by Skeef79

typedef long long ll;
typedef long double ld;
typedef unsigned long long ull;

#pragma warning(disable : 4996)
#pragma comment(linker, "/STACK:16777216")
#define pb push_back
#define en '\n'
#define for0(i,n) for(int i = 0;i<n;i++)
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define vec vector
#define pii pair<int,int>
#define pll pair<ll,ll>

using namespace std;

const int INF = 2000000000;
const ll LINF = 2000000000000000000;

template<typename T> void print(vector<T>& a)
{
	for (int i = 0; i < a.size(); i++)
		cout << a[i] << ' ';
	cout << en;
}

template<typename T> void print(deque<T>& a)
{
	for (int i = 0; i < a.size(); i++)
		cout << a[i] << ' ';
	cout << en;
}

template<typename T> void print(vector<vector<T>>& a)
{
	for (int i = 0; i < a.size(); i++)
	{
		for (int j = 0; j < a[i].size(); j++)
			cout << a[i][j] << ' ';
		cout << en;
	}
}

template <typename T> void input(vector<T>& a)
{
	for (int i = 0; i < a.size(); i++)
		cin >> a[i];
}

template<typename T> void input(deque<T>& a)
{
	for (int i = 0; i < a.size(); i++)
		cin >> a[i];
}

template<typename T> void input(vector<vector<T>>& a)
{
	for (int i = 0; i < a.size(); i++)
		for (int j = 0; j < a[i].size(); j++)
			cin >> a[i][j];
}

const ll mod = 1e9 + 7;

void solve()
{
	int n;
	cin >> n;
	vector<ll>a(n);
	input(a);

	ll ans = 0;
	vector<ll> cnt1(60);
	vector<ll>cnt0(60);

	for(auto to:a)
	{
		for(int i =0 ;i<60;i++)
			if (to&(ll(1) << i))
				cnt1[i]++;
			else
				cnt0[i]++;

	}

	for (int i = 0; i < n; i++)
	{
		for (int bit = 0; bit < 60; bit++)
		{
			if (a[i] & (ll(1)<<bit))
			{
				cnt1[bit]--;
				ans = (ans%mod + (cnt0[bit]) % mod*(ll(1) << bit) % mod);
				ans = ans % mod;

			}
			else
			{
				cnt0[bit]--;
				ans = (ans%mod + (cnt1[bit] % mod)*(ll(1) << bit) % mod) % mod;
			}

		}

	}
	cout << ans%mod;

}

int main()
{
	ios::sync_with_stdio(false);
	cin.tie(0);
	cout.tie(0);

#ifdef _DEBUG
	freopen("input.txt", "r", stdin);
#endif

	int tst = 1;
	//cin >> tst;
	while (tst--)
		solve();
}