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)

{-# OPTIONS_GHC -O2 #-}
{-# LANGUAGE OverloadedStrings #-}
{-# LANGUAGE ScopedTypeVariables #-}
{-# LANGUAGE LambdaCase #-}
{-# LANGUAGE BangPatterns #-}
{-# LANGUAGE TupleSections #-}

module Main where

import           Data.List
import           Control.Monad
import           Debug.Trace
import qualified Data.ByteString.Char8         as BC
import           Data.Maybe                     ( fromJust, fromMaybe )
import qualified Data.Set                      as S
import qualified Data.IntMap.Strict            as IM
import qualified Data.IntMap.Lazy            as IML
import qualified Data.Map.Strict               as M
import           Data.Char
import qualified Data.Array.IArray as A
import qualified Data.Array.Unboxed as UA
import Data.Bits
import Control.Monad.State.Strict
import qualified Data.Array.ST as STA
import qualified Data.Array.IO as IOA
import qualified Data.Array.MArray as MA
import Control.Monad.ST
import System.IO (stdin)
import Control.Arrow
import qualified Data.Vector as V
import qualified Data.Vector.Unboxed as UV
import qualified Data.Vector.Generic as GV
import qualified Data.Vector.Mutable as MV
import Data.Ix
import Data.Ord (Down(Down))
import qualified Data.Sequence as Seq
import Data.Foldable (toList)
import Data.Fixed

debug = False

ts :: Show a => a -> a
ts a = if debug then traceShowId a else a


readTuple2 :: IO (Int, Int)
readTuple2 = do
    [a, b] <- readInts
    return (a, b)

readTuple3 :: IO (Int, Int, Int)
readTuple3 = do
    [a, b, c] <- readInts
    return (a, b, c)


readInt :: IO Int
readInt = fst . fromJust . BC.readInt <$> BC.getLine

readInts :: IO [Int]
readInts = map (fst . fromJust . BC.readInt) . BC.words <$> BC.getLine

readIntV :: Int -> IO (UV.Vector Int)
readIntV n = GV.unfoldrN n (fmap (fmap BC.tail) . BC.readInt) <$> BC.getLine

readIntegersV :: Int -> IO (V.Vector Integer)
readIntegersV n = GV.unfoldrN n (fmap (fmap BC.tail) . BC.readInteger) <$> BC.getLine

readIntegers :: IO [Integer]
readIntegers = map (fst . fromJust . BC.readInteger) . BC.words <$> BC.getLine

split :: (a -> Bool) -> [a] -> [[a]]
split f [] = []
split f as =
    let (fo, la) = span f as
        las      = case la of
            [] -> []
            xs -> split f $ tail xs
    in  case fo of
            [] -> las
            xs -> xs : las

modN = 1000000007

pow :: Num a => a -> Int -> a
pow base 0 = 1
pow base 1 = base
pow base time
    | odd time = let
        a = pow base (div time 2)
        in
        a * a * base
    | otherwise = let
        a = pow base (div time 2)
        in
        a * a

inv :: ModNum -> ModNum
inv a = pow a $ modN - 2

newtype ModNum = ModNum {getInt :: Int} deriving (Show, Eq, Ord)
instance Num ModNum where
    (+) (ModNum a) (ModNum b) = ModNum $ mod (a + b) modN
    (-) (ModNum a) (ModNum b)
            | a < b = (ModNum $ a + modN) - ModNum b
            | otherwise = ModNum $ mod (a - b) modN
    (*) (ModNum a) (ModNum b) = ModNum $ mod (a * b) modN
    abs (ModNum a)
        | a < 0 = abs . ModNum $ a + modN
        | otherwise = ModNum a
    signum (ModNum a) = ModNum $ signum a
    fromInteger i = abs . ModNum . fromIntegral $ mod i (fromIntegral modN)


solve :: [Int] -> Int
solve as = getInt . sum $ ketaSum <$> [0..60]  where
  base :: ModNum
  base = fromIntegral 2
  getOneAndZeroNum :: Int -> (Int, Int)
  getOneAndZeroNum keta = foldl' (\(one, zero) a -> if testBit a keta then (one+1, zero) else (one, zero+1)) (0, 0) as
  ketaSum :: Int -> ModNum
  ketaSum keta = let
    (one, zero) = getOneAndZeroNum keta
    in
    base ^ keta * (fromIntegral one * fromIntegral zero)


main :: IO ()
main =
  getLine *> readInts >>= print . solve