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 Kotlin (1.3.71) (judge verdict: Accepted)

import java.io.PrintWriter

fun next() = readLine()!!
fun nextInt() = next().toInt()
fun nextLong() = next().toLong()
fun nextDouble() = next().toDouble()
fun nextList() = next().split(" ")
fun nextIntList() = nextList().map(String::toInt)
fun nextLongList() = nextList().map(String::toLong)
fun nextDoubleList() = nextList().map(String::toDouble)

val pw = PrintWriter(System.out)
fun print(s: Any = "") = pw.print(s)
fun println(s: Any = "") = pw.println(s)

fun <T> Iterable<T>.join(separator: CharSequence = ", ", prefix: CharSequence = "", postfix: CharSequence = "") = joinToString(separator, prefix, postfix)
fun <T> Array<T>.join(separator: CharSequence = ", ", prefix: CharSequence = "", postfix: CharSequence = "") = joinToString(separator, prefix, postfix)

fun main(args: Array<String>) {
    main()
    pw.flush()
}

fun main() {
    val N = nextInt()
    val A = nextLongList().toMutableList()
    var ans = MInt2(0)
    var base = MInt2(1)
    for (d in 1..60) {
        var one = 0L
        var zero = 0L
        for (i in A.indices) {
            if (A[i] and 1 == 0L) {
                zero++
            } else {
                one++
            }
            A[i] = A[i] shr 1
        }
        ans += base * (MInt2(one) * zero)
        base *= 2
    }
    println(ans)
}

class MInt2 {
    private val MOD = 1000000007L
    var v: Long

    constructor(v: Long) {
        this.v = v % MOD
    }

    constructor(v: Int) {
        this.v = v.toLong() % MOD
    }

    operator fun plus(b: MInt2): MInt2 {
        val a = MInt2(v)
        a.v += b.v
        if (a.v >= MOD) a.v -= MOD
        return a
    }

    operator fun plus(b: Int) = plus(MInt2(b))
    operator fun plus(b: Long) = plus(MInt2(b))

    operator fun minus(b: MInt2): MInt2 {
        val a = MInt2(v)
        a.v -= b.v
        if (a.v < 0) a.v += MOD
        return a
    }

    operator fun minus(b: Int) = minus(MInt2(b))
    operator fun minus(b: Long) = minus(MInt2(b))

    operator fun times(b: Long) = times(MInt2(b))
    operator fun times(b: MInt2): MInt2 {
        val a = MInt2(v)
        a.v *= b.v
        a.v %= MOD
        return a
    }

    fun pow(N: Int) = pow(N.toLong())

    fun pow(N: Long): MInt2 {
        var ans = MInt2(1)
        var a = this
        var n = N
        while (n > 0) {
            if (n.and(1) == 1L) {
                ans *= a
            }
            a *= a
            n = n.shr(1)
        }
        return ans
    }

    override fun toString(): String {
        return v.toString()
    }
}