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 Go (1.6) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	N := nextInt()
	bits := make([]mint, 64)

	for i := 0; i < N; i++ {
		a := nextUint64()

		for j := 0; j <= 60; j++ {
			bits[j] += mint(nthbit(a, j))
		}
	}

	s := mint(0)

	for i := 0; i <= 60; i++ {
		b := mint(2).pow(mint(i))
		s = s.add(b.mul(bits[i]).mul(mint(N) - bits[i]))
	}

	fmt.Println(s)
}

func nthbit(a uint64, n int) int { return int((a >> uint(n)) & 1) }

type mint uint64

var mod = mint(1e9 + 7)

// add は a + bを返します
func (a mint) add(b mint) mint {
	return (a + b) % mod
}

// sub は a - bを返します
func (a mint) sub(b mint) mint {
	return (a - b + mod) % mod
}

// mul は a * bを返します
func (a mint) mul(b mint) mint {
	return (a * (b % mod)) % mod
}

// div は a/bを返します
func (a mint) div(b mint) mint {
	return a.mul(b.inv())
}

// inv は aの逆元を返します
func (a mint) inv() mint {
	// 拡張ユークリッドの互除法
	b := mod
	u := mint(1)
	v := mint(0)
	for b > 0 {
		t := a / b
		a -= t * b
		a, b = b, a
		u -= t * v
		u, v = v, u
	}
	return (u + mod) % mod
}

// pow は a ^ bを返します
func (a mint) pow(b mint) mint {
	ans := mint(1)

	for b != 0 {
		if b&1 == 1 {
			ans = ans.mul(a)
		}
		a = a.mul(a)
		b = b >> 1
	}
	return ans
}

var stdin = initStdin()

func initStdin() *bufio.Scanner {
	bufsize := 1 * 1024 * 1024 // 1 MB
	var stdin = bufio.NewScanner(os.Stdin)
	stdin.Buffer(make([]byte, bufsize), bufsize)
	stdin.Split(bufio.ScanWords)
	return stdin
}

func nextString() string {
	stdin.Scan()
	return stdin.Text()
}

func nextBytes() []byte {
	stdin.Scan()
	return stdin.Bytes()
}

func nextInt() int {
	i, _ := strconv.Atoi(nextString())
	return i
}

func nextUint64() uint64 {
	i, _ := strconv.ParseUint(nextString(), 10, 64)
	return i
}