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>
using namespace std;

typedef long long ll;
const int maxn = 3e5+100,MOD = 1e9+7;
ll arr[maxn],bits[maxn][2],tt[maxn];

int main() {
    ll n,ans = 0;
    tt[0] = 1;
    for(int i=1; i<=60; i++) {
        tt[i] = tt[i-1]*2%MOD;
    }
    //slove()
    scanf("%lld",&n);
    for(int i=0; i<n; i++) scanf("%lld",&arr[i]);
	for(int k=0; k<=60; k++) {
		for(int i=0; i<n; i++) {
			bits[k][arr[i]%2]++;
			arr[i]/=2;
		}
		ans = (ans+bits[k][0]*bits[k][1]%MOD*tt[k]%MOD)%MOD;
	}
	ans %= MOD;
    printf("%lld\n",ans);
    return 0;
}