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: Time Limit Exceeded)

{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE CPP #-}
module Main where

import qualified Data.Vector as V 
import qualified Data.Map.Strict as M
import Control.Monad
import qualified Data.ByteString.Char8 as BS
import Data.Maybe
import Data.Bits
import Data.List (foldl')
dump :: (Show a) => a -> IO()
#if __GLASGOW_HASKELL__ >= 800
dump x = print x
#else
dump _ = pure ()
#endif

-- "101010" -> [1,0,1,0,1,0]
readToList :: String -> [Int]
readToList [] = []
readToList (x:xs) = read [x] : readToList xs

-- "10 10 10" -> [10, 10, 10]
readvec :: IO [Int]
readvec = (fmap (read . BS.unpack) . BS.words) <$> BS.getLine

newtype UF a = UF (M.Map a a) deriving (Show) -- Map node parent

makeuf :: Int -> UF Int
makeuf n = let m = M.fromList $ zip [0..n] [0..n]
                in UF m

union :: (Eq a, Ord a) => a -> a -> UF a -> UF a
union l r uf@(UF m) = let lp = find l uf
                          rp = find r uf
                      in if lp == rp
                         then uf
                         else if size l uf < size r uf
                              then UF $ M.update (const $ Just rp) lp m
                              else UF $ M.update (const $ Just lp) rp m

find :: (Eq a, Ord a) => a -> UF a -> a
find x uf@(UF m) = let px = m M.! x
                in if px == x
                   then px
                   else find px uf -- TODO 貼り直し

size :: (Eq a, Ord a) => a -> UF a -> Int
size x (UF m) = M.size $ M.filter (\par -> par==x) m

base :: Int
base = 10 ^ 9 + 7


forn :: (Num a, Enum a, Monad m) => a -> (a -> m b) -> m [b]
forn x = forM [0..(x-1)]

count :: (Eq a) => a -> [a] -> Int
count y = length . filter (== y)

main :: IO()
main = do
  [n] <- readvec
  xs <- readvec
  ress <- forn 60 $ \offset -> do
            let a = shift 1 offset
            let ys = map (a .&.) xs
            let zeros = count 0 $ ys
            let ones = length $ filter (/= 0) $ ys
            return $ zeros * ones `mod` base
  print $ foldl' (\r x -> (r*2+x) `mod` base) 0 $ reverse ress