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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
  input = input.split("\n");
  var N = input[0];
  var A = input[1];
  A = A.split(" ").map(Number);
  for(var i=0;i<N;i++){
    A[i] = A[i].toString(2);
    A[i] = ( '000000000000000000000000000000000000000000000000000000000000' + A[i] ).slice( -60 );
  }
  var sum = [];
  for(var j=1;j<=60;j++){
    var count = 0;
    for(var k=0;k<N;k++){
    var n = A[k];
    if(n.substr(-1*j,1) == 1){
    count++;
    }
      //console.log(j,k,n.substr(-1*j,1))
  }
        sum.push(count);
  }
  var ans = 0;
  for(var o=0;o<60;o++){
  ans += sum[o]*(N-sum[o])*Math.pow(2,o);
    if(ans>=1000000007){
    ans = ans%1000000007;
    }
  }
  //console.log(sum,A);
  console.log(ans);
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));