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: Time Limit Exceeded)

// i hope i get better                                                           
#include <bits/stdc++.h>
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define all(x) x.begin(), x.end()
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
const int sz=3e5+9;
ll a[sz];
ll cs[65][sz];
ll mod=1e9+7;
ll add(ll a,ll b){return ((a%mod+b%mod)%mod+mod)%mod;}
ll mul(ll a,ll b){return (a%mod*b%mod)%mod;}
ll ans;
int n;

int main(){
	scanf("%d",&n);
	for(int i=1;i<=n;i++){
		scanf("%lld",&a[i]);
	}
	for(int i=n;i>=1;i--){
		for(int j=0;j<64;j++){
			cs[j][i]=cs[j][i+1]+((a[i]>>j)&1);
		}
	}
	for(int i=1;i<n;i++){
		ll tot=n-i;
		for(int j=0;j<64;j++){
			ll cnt=cs[j][i+1];
			if((a[i]>>j)&1) ans=add(ans,mul(1ll<<j,tot-cnt));
			else ans=add(ans,mul(1ll<<j,cnt));
		}
	}
	printf("%lld",ans);
	return 0;
}