Problem:
Score : 200 points

Problem Statement

There are N bags of biscuits. The i-th bag contains A_i biscuits.

Takaki will select some of these bags and eat all of the biscuits inside.
Here, it is also possible to select all or none of the bags.

He would like to select bags so that the total number of biscuits inside is congruent to P modulo 2.
How many such ways to select bags there are?

Constraints

1 \leq N \leq 50

P = 0 or 1

1 \leq A_i \leq 100

Input

Input is given from Standard Input in the following format:

N P
A_1 A_2 ... A_N

Output

Print the number of ways to select bags so that the total number of biscuits inside is congruent to P modulo 2.

Sample Input 1

2 0
1 3

Sample Output 1

2

There are two ways to select bags so that the total number of biscuits inside is congruent to 0 modulo 2:

Select neither bag. The total number of biscuits is 0.

Select both bags. The total number of biscuits is 4.

Sample Input 2

1 1
50

Sample Output 2

0

Sample Input 3

3 0
1 1 1

Sample Output 3

4

Two bags are distinguished even if they contain the same number of biscuits.

Sample Input 4

45 1
17 55 85 55 74 20 90 67 40 70 39 89 91 50 16 24 14 43 24 66 25 9 89 71 41 16 53 13 61 15 85 72 62 67 42 26 36 66 4 87 59 91 4 25 26

Sample Output 4

17592186044416

Solution in Kotlin (1.3.71) (judge verdict: Runtime Error)

import java.io.PrintWriter
import java.util.*
import kotlin.math.pow

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 Int.pow(n: Int) = pow(n.toLong())
fun Int.pow(n: Long) = toDouble().pow(n.toDouble()).toLong()
fun Long.pow(n: Int) = pow(n.toLong())
fun Long.pow(n: Long) = toDouble().pow(n.toDouble()).toLong()

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

fun main() {
    val (N, P) = nextIntList()
    val A = nextIntList()
    val E = A.count { it % 2 == 0 }.toLong()
    val O = N - E
    val combi = Combination(50)
    if (P == 0) {
        val ans = 2.pow(E) * (0..O step 2).map { combi(O, it) }.sum()
        println(ans)
    } else {
        val ans = 2.pow(E) * (1..O step 2).map { combi(O, it) }.sum()
        println(ans)
    }
}

class Combination(n: Int) {
    private val fact = Array<HInt?>(n + 1) { null }

    init {
        fact[0] = HInt(1)
        (1..n).forEach { i -> fact[i] = fact[i - 1]!! * i }
    }

    operator fun invoke(n: Long, k: Long) = invoke(n.toInt(), k.toInt())
    operator fun invoke(n: Int, k: Int): Long {
        if (k < 0 || n < k) return 0L
        return (fact[n]!! / (fact[k]!! * fact[n - k]!!)).toLong()
    }
}

class HInt {
    private val map = HashMap<Long, Int>()

    constructor(n: Int) : this(n.toLong())
    constructor(n: Long) : this(primefact(n))
    private constructor(_map: Map<Long, Int>) {
        map.putAll(_map)
    }

    operator fun times(n: Int) = times(n.toLong())
    operator fun times(n: Long) = times(primefact(n))
    operator fun times(n: HInt) = times(n.map)

    private fun times(_map: Map<Long, Int>): HInt {
        val res = HInt(map)
        _map.forEach { (k, v) ->
            val ex = res.map[k] ?: 0
            res.map[k] = ex + v
        }
        return res
    }

    operator fun div(n: Int) = div(n.toLong())
    operator fun div(n: Long) = div(primefact(n))
    operator fun div(n: HInt) = div(n.map)

    private fun div(_map: Map<Long, Int>): HInt {
        val res = HInt(map)
        _map.forEach { (k, v) ->
            val ex = res.map[k] ?: 0
            res.map[k] = ex - v
        }
        return res
    }

    fun toLong() = map.entries.map { (k, v) -> k.pow(v) }.reduce { a, b -> a * b }

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

fun primefact(n: Long): HashMap<Long, Int> {
    val map = HashMap<Long, Int>()
    var tmp = n
    for (i in 2L..(Math.sqrt(n.toDouble()).toLong() + 1)) {
        if (tmp % i == 0L) {
            var cnt = 0
            while (tmp % i == 0L) {
                tmp /= i
                cnt++
            }
            map[i] = cnt
        }
        if (tmp == 1L) break
    }
    if (tmp != 1L) {
        map[tmp] = 1
    }
    return map
}