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)

#include<bits/stdc++.h>
#define int long long
#define mod 1000000007
using namespace std;
#define deb(x) cout<<#x<<" = "<<x<<"\n";
 
signed main()
{
	#ifndef ONLINE_JUDGE
	freopen("input.txt", "r", stdin);
	//freopen("output.txt", "w", stdout);
	#endif
	/************************************/
	
	int n ;cin>>n;
	int a[n];
	for(int i=0; i<n; i++) cin>>a[i];
	
	int ans = 0 ,t = 1;
	for(int bit=0; bit<63; bit++)
	{
		int set = 0, unset =0;
		for(int i=0; i<n; i++)
		{
			if(a[i]&1) set++;
			else unset++;
			
			a[i] >>= 1; 
		}
		ans += (set * unset * (t % mod)) % mod;
		t *= 2; t%= mod;
		ans %= mod;
	}
	cout<<ans<<"\n";
	
	
}