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 7.10.3) (judge verdict: Accepted)

import Data.Char
import Data.List
import Data.Bits
import qualified Data.ByteString.Char8 as BS

main :: IO ()
main = do
  n <- head.parseLine <$> BS.getLine
  as <- parseLine <$> BS.getLine
  print $ solve n as
  where
    parseLine = unfoldr (BS.readInt . BS.dropWhile isSpace)

solve :: Int -> [Int] -> Integer
solve n as = (`mod` (10^9+7)) . (calcEachBitResults n) . aggregateBits $ as

aggregateBits :: [Int] -> [Int]
aggregateBits as = map (countBits as) [0..(bitLength as-1)] 

bitLength :: [Int] -> Int
bitLength as = finiteBitSize (maximum as) - countLeadingZeros (maximum as)

countBits :: [Int] -> Int -> Int
countBits as d = length . filter (flip testBit d) $ as

calcEachBitResults :: Int -> [Int] -> Integer
calcEachBitResults n = sum . zipWith (\d x -> 2^d*x) [0..] . map ((\x -> x * (n'-x)).fromIntegral)
  where
    n' = fromIntegral n