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.Bits
import Data.List
import qualified Data.ByteString.Char8 as B

solve :: [Int] -> Mint
solve as = sum $ map f [0..59] where
  f :: Int -> Mint
  f i = M one * M zro * 2^i where
    one = length $ filter (`testBit` i) as
    zro = length as - one

main=getLine>>readIntsLn>>=print.solve

modulus = 10^9+7
newtype Mint = M Int
instance Enum Mint where
  fromEnum(M a) = a
  toEnum a = M$ mod a modulus
instance Num Mint where
  (M a)+(M b) = toEnum$ a+b
  (M a)*(M b) = toEnum$ a*b
  (M a)-(M b) = toEnum$ a-b
  fromInteger = toEnum . fromInteger
  abs = id
  signum = const (M 1)
instance Show Mint where
  show (M a) = show a

readIntsLn
  = unfoldr (B.readInt . B.dropWhile(==' ')) <$> B.getLine