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 Common Lisp (SBCL 1.1.14) (judge verdict: Time Limit Exceeded)

;; D - Xor Sum 4

(defparameter *modulus* (+ (expt 10 9) 7))
(defparameter *max-bits* 60)

(defun main ()
  (let* ((N (read))
         (A (loop repeat N collect (read))))
    (print (solve N A))
    (fresh-line)))

(defun solve (N A)
  ; 各桁を集約
  (reduce #'(lambda (l h) (mod (+ l (ash h 1)) *modulus*))
    ; 2進各桁のXORの総和 (= 1の個数 * 0の個数)
    (map 'vector #'(lambda (m) (* m (- N m)))
      ; 各数を2進各桁のベクトルに変換し和 (2進各桁の1の個数) を求める
      (loop with vec = (to-bit-vector (car A))
            for elem in (cdr A)
            do (map-into vec #'+ vec (to-bit-vector elem))
            finally (return vec)))
    :from-end t))

(defun to-bit-vector (n)
  "整数nを2進各桁の配列 (最下位が前) に変換"
  (loop with vec = (make-array *max-bits*)
        for i from 0 below *max-bits*
        for m = n then (ash m -1) do (setf (aref vec i) (mod m 2))
        finally (return vec)))

(compile 'to-bit-vector)
(compile 'solve)

(main)