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 Haskell (GHC 8.8.3) (judge verdict: Time Limit Exceeded)

import Data.Bits
import Data.Bool
import Data.List   

readInt = read :: String -> Integer

main = do
  n <- readInt <$> getLine
  ns <- map readInt . words <$> getLine
  --let n = 10
  --let ns = [3 ,14 ,159 ,2653 ,58979 ,323846 ,2643383 ,27950288 ,419716939 ,9375105820]  :: [Integer]
  let bits e = map (bool 0 1 . testBit e) [0 :: Int ..64]
  let totalbits1 = foldl1 (zipWith (+)) $  map bits ns
  let totalbits = map (\e -> e * (n - e)) totalbits1
  let pows = map (\b -> (bit b) `mod` (10^9 + 7)  :: Integer) [0 ..64]
  let ans =  sum $  zipWith (*) pows totalbits

  print $ ans `mod` (10^9 + 7)