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>
#pragma GCC optimize("Ofast")
#define int long long
#define mod (int)(1e9+7)
#define inf (int)(3e18)
#define rep(i,n) for(int i=0;i<n;i++)
#define REP(i,n) for(int i=1;i<n;i++)
#define P std::pair<int,int>
#define PiP std::pair<int,std::pair<int,int>>
#define all(v) v.begin(),v.end()
#define mkp std::make_pair
#define prique(T) std::priority_queue<T,vector<T>,greater<T>>
using namespace std;
template<class T> inline void chmax(T& a, T b) { a = std::max(a, b); }
template<class T> inline void chmin(T& a, T b) { a = std::min(a, b); }

bool prime(int x) {
	for (int i = 2; i * i <= x; i++) {
		if (x % i == 0)return false;
	}
	return x != 1;
}
int gcd(int x, int y) {
	if (y == 0)return x;
	return gcd(y, x % y);
}
int lcm(int x, int y) {
	return x / gcd(x, y) * y;
}
int kai(int x, int y) {
	int res = 1;
	for (int i = x - y + 1; i <= x; i++) {
		res *= i; res %= mod;
	}
	return res;
}
int mod_pow(int x, int y, int m) {
	int res = 1;
	while (y > 0) {
		if (y & 1) {
			res = res * x % m;
		}
		x = x * x % m;
		y >>= 1;
	}
	return res;
}
int comb(int x, int y) {
	if (y > x)return 0;
	return kai(x, y) * mod_pow(kai(y, y), mod - 2, mod) % mod;
}
int get_rand(int MIN, int MAX) {
	std::random_device rnd;
	std::mt19937 mt32(rnd());
	std::uniform_int_distribution<int>engine(MIN, MAX);
	return engine(mt32);
}
/*--------Library Zone!--------*/


int n;
int a[300005];
signed main() {
	cin >> n;
	rep(i, n)cin >> a[i];
	int ans = 0;
	rep(i, 62) {
		int one = 0, zero = 0;
		rep(j, n) {
			if (a[j] >> i & (int)1)one++;
			else zero++;
		}
		ans += (1ll << i) % mod * one % mod * zero % mod;
		ans %= mod;
	}
	cout << ans << endl;
}