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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)


import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.*;
import java.util.stream.IntStream;
import java.util.stream.LongStream;

public class Main {

    public Main() throws IOException {
    }

    public static void main(String[] args) throws IOException {
        new Main().solve();
    }

    //    private final InputStream in = Files.newInputStream(Paths.get("C:\\Users\\ryo.suzuki\\Downloads\\02.txt"));
    private final InputStream in = System.in;
    private final PrintWriter out = new PrintWriter(System.out);
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;

    private void solve() throws IOException {
        try {
//            solveA();
//            solveB();
            solveC();
//            solveD();
//            solveE();
//            solveF();
        } finally {
            if (in != null) {
                in.close();
            }
            if (out != null) {
                out.flush();
                out.close();
            }
        }

    }

    // mods
    long MOD = (long) Math.pow(10, 9) + 7;

    /**
     * https://atcoder.jp/contests/abc134/tasks/abc134_a
     * ABC134-A
     */
    private void solveA() {
        out.println(3 * (int) Math.pow(nextInt(), 2));
    }

    /**
     * https://atcoder.jp/contests/agc040/tasks/agc040_a
     * AGC040-A
     * <  >  >   >   <   <  >   <  <  <  <  <  >  >  >  <
     * 0  1  0  -1  -2  -1  0  -1  0  1  2  3  4  3  2  1  2     0-indexedを起点として±しただけ
     * 0  3  2   1   0   1  2   1  2  3  4  5  6  5  4  3  4  46 一番最小を0に押し上げる（NG）
     * 0  3  2   1   0   1  2   0  1  2  3  4  5  2  1  0  1  28
     * 0  1  0   0   0   1  2   0  1  2  3  4  5  0  0  0  1 左からのみ計算
     * 0  3  2   1   0   0  1   0  0  0  0  0  3  2  1  0  0 右からのみ計算
     */
    private void solveB() {
        String s = next();
        int[] l = new int[s.length() + 1];
        for (int i = 1; i < s.length() + 1; i++) {
            switch (s.charAt(i - 1)) {
                case '<':
                    l[i] = i != 0 ? l[i - 1] + 1 : 1;
                    break;
                case '>':
                    l[i] = 0;
                    break;
            }
        }
        int[] r = new int[s.length() + 1];
        for (int i = 1; i < s.length() + 1; i++) {
            int idx = s.length() - i;
            switch (s.charAt(idx)) {
                case '<':
                    r[idx] = 0;
                    break;
                case '>':
                    r[idx] = i != 0 ? r[idx + 1] + 1 : 1;
                    break;
            }
        }
        long res = 0;
        for (int i = 0; i < l.length; i++) {
            res = res + (long) Math.max(l[i], r[i]);
        }
        out.println(res);
    }

    /**
     * https://atcoder.jp/contests/agc017/tasks/agc017_a
     * AGC017-A
     */
    private void solveC() {
        int n = nextInt();
        int p = nextInt();
        int[] a = IntStream.range(0, n).map(i -> nextInt()).toArray();
        int cntEven = 0;
        int cntOdd = 0;
        for (int item : a) {
            if (item % 2 == 0)
                cntEven++;
            else
                cntOdd++;
        }
        if (cntEven > 0 && cntOdd == 0) {
            if (p == 0)
                out.println(pow(2, n));
            else if (p == 1)
                out.println(0);
        } else if (cntEven == 0 && cntOdd > 0) {
            if (p == 0)
                out.println(pow(2, n - 1));
            else if (p == 1)
                out.println(pow(2, n - 1));
        } else if (cntEven > 0 && cntOdd > 0) {
            if (p == 0)
                out.println(pow(2, n - 1));
            else if (p == 1)
                out.println(pow(2, n - 1));
        } else {
            out.println(0);
        }
    }

    /**
     * https://atcoder.jp/contests/abc006/tasks/abc006_3
     * ABC006-C
     */
    private void solveD() {
        int n = nextInt();
        int m = nextInt();
        int j = 0;
        if (m % 2 != 0)
            j = 1;
        for (int i = 0; i <= n; i++) {
            int k = n - (i + j);
            if (k < 0)
                continue;
            int tmp = i * 2 + j * 3 + k * 4;
            if (tmp == m) {
                out.println(i + " " + j + " " + k);
                return;
            }
        }
        out.println("-1 -1 -1 ");
    }

    /**
     * https://atcoder.jp/contests/abc126/tasks/abc126_e
     * UnionFind
     * ABC126-E
     */
    private void solveE() {
        int n = nextInt();
        int m = nextInt();
        /*
        A + B + Z => 偶数(mod 2 =0)
        Z => 1 or 2
        A + B = Z (mod 2)
        -> A + B = 偶数なら、Z=2
         */
        UnionFind unionFind = new UnionFind(n);
        IntStream.range(0, m).forEach(i ->
                {
                    unionFind.unite(nextInt() - 1, nextInt() - 1);
                    nextInt();
                }
        );
        out.println(unionFind.getParentsNum());
    }

    public static class UnionFind {
        int[] pars;

        public UnionFind(int n) {
            pars = new int[n];
            Arrays.fill(pars, -1);
        }

        public int getChilds(int n) {
            int wk = getRoot(n);
            return pars[wk];
        }

        public int getRoot(int n) {
            if (pars[n] < 0)
                return n;
            return pars[n] = getRoot(pars[n]);
        }

        public boolean isSame(int a, int b) {
            return getRoot(a) == getRoot(b);
        }

        private int getSize(int a) {
            return -pars[getRoot(a)];
        }

        public void unite(int a, int b) {
            int wkA = getRoot(a);
            int wkB = getRoot(b);
            if (wkA == wkB)
                return;

            if (getSize(wkA) < getSize(wkB)) {
                int tmp = wkA;
                wkA = wkB;
                wkB = tmp;
            }
            pars[wkA] = pars[wkA] + pars[wkB];
            pars[wkB] = wkA;
        }

        public long getParentsNum() {
            return Arrays.stream(pars).filter(i -> i < 0).count();
        }
    }

    private void solveF() {

    }

    static final long CONST_INF = Long.MAX_VALUE / 4;


    private static class VectorCalculation {
        /**
         * 点Pと線(AB)の距離
         *
         * @param p
         * @param a
         * @param b
         * @return
         */
        private double distanceDotAndLine(DoublePair p, DoublePair a, DoublePair b) {
            DoublePair ab = new DoublePair(b.x - a.x, b.y - a.y);
            DoublePair ap = new DoublePair(p.x - a.x, p.y - a.y);

            // ベクトルAB、APの外積の絶対値が平行四辺形Dの面積になる
            double d = Math.abs(crossVector(ab, ap));

            double l = distanceVertex(a, b); // AB間の距離

            double h = d / l;
            return h;
        }

        /**
         * 2点間距離
         *
         * @param p1
         * @param p2
         * @return
         */
        private double distanceVertex(DoublePair p1, DoublePair p2) {
            double dx = p1.x - p2.x;
            double dy = p1.y - p2.y;
            return Math.sqrt(dx * dx + dy * dy);
        }

        /**
         * ベクトル外積
         *
         * @param vl
         * @param vr
         * @return
         */
        private double crossVector(DoublePair vl, DoublePair vr) {
            return vl.x * vr.y - vl.y * vr.x;
        }
    }

    private static class DoublePair implements Comparable<DoublePair> {
        double x;
        double y;

        public DoublePair(double k, double v) {
            this.x = k;
            this.y = v;
        }

        public int compareTo(DoublePair pair) {
            return Double.compare(this.y, pair.y);
        }
    }

    private static class SimplePair implements Comparable<SimplePair> {
        long k;
        long v;

        public SimplePair(int k, int v) {
            this.k = k;
            this.v = v;
        }

        public SimplePair(long k, long v) {
            this.k = k;
            this.v = v;
        }

        public int compareTo(SimplePair pair) {
            return Long.compare(this.v, pair.v);
        }
    }


    private static class SimpleGraphNode {
        private int n;
        private Map<Integer, Integer> childs;

        public SimpleGraphNode(int n) {
            this.n = n;
            childs = new HashMap<Integer, Integer>();
        }

        public void addChild(int child, int d) {
            this.childs.put(child, d);
        }
    }

    private static class SimpleGraph {

        private Map<Integer, SimpleGraphNode> graph;

        public SimpleGraph(int[][] list) {
            graph = new HashMap<Integer, SimpleGraphNode>();
            Arrays.stream(list).forEach(l -> {
                int a = l[0];
                int b = l[1];
                int d = l[2];
                graph.put(a, graph.getOrDefault(a, new SimpleGraphNode(a)));
                graph.get(a).addChild(b, d);
                graph.put(b, graph.getOrDefault(b, new SimpleGraphNode(b)));
                graph.get(b).addChild(a, d);
            });
        }

        public SimpleGraphNode getNode(int i) {
            return graph.getOrDefault(i, new SimpleGraphNode(-1));
        }

    }

    private static class GraphNode {
        private long n;
        private Map<Long, SimplePair> childs;

        public GraphNode(long n) {
            this.n = n;
            childs = new TreeMap<Long, SimplePair>();
        }

        /**
         * not update
         *
         * @param child
         * @param d
         */
        public void addChild(long child, long d) {
            this.childs.put(child, this.childs.getOrDefault(child, new SimplePair(child, d)));
        }

        public SimplePair getChild(long child) {
            return this.childs.getOrDefault(child, new SimplePair(child, CONST_INF));
        }
    }

    private static class Graph {

        private Map<Long, GraphNode> graph;
        int n;

        /**
         * @param n    頂点数
         * @param list
         */
        public Graph(int n, int[][] list) {
            this.n = n;
            graph = new HashMap<Long, GraphNode>();
            /*
            隣接行列作成
            0-indexed
             */
            Arrays.stream(list).forEach(l -> {
                long a = l[0] - 1;
                long b = l[1] - 1;
                long d = l[2];
                graph.put(a, graph.getOrDefault(a, new GraphNode(a)));
                graph.get(a).addChild(b, d);
                graph.put(b, graph.getOrDefault(b, new GraphNode(b)));
                graph.get(b).addChild(a, d);
            });
            /*
            たどり着けない場所はCONST_INFで埋める
            自分へはCOST=0でたどり着ける
             */
            for (long i = 0; i < n; i++) {
                graph.put(i, graph.getOrDefault(i, new GraphNode(i)));
                GraphNode node = graph.get(i);
                for (int j = 0; j < n; j++) {
                    if (i == j)
                        node.addChild(j, 0L);
                    else
                        node.addChild(j, CONST_INF);
                }
            }
        }

        /**
         * ワーシャルフロイド
         */
        public void warshallFloyd() {
            for (long k = 0; k < n; k++) {
                for (long i = 0; i < n; i++) {
                    for (long j = 0; j < n; j++) {
                        long min = Math.min(graph.get(i).getChild(j).v, graph.get(i).getChild(k).v + graph.get(k).getChild(j).v);
                        graph.get(i).getChild(j).v = min;
                    }
                }
            }
        }

        public void partialUpdateAndWarshallFloyd(long x, long y, long w) {
            if (graph.get(x).getChild(y).v > w)
                graph.get(x).getChild(y).v = graph.get(y).getChild(x).v = w;
            long[] l = {x, y};
            for (long k : l) {
                for (long i = 0; i < n; i++) {
                    for (long j = 0; j < n; j++) {
                        if (graph.get(i).getChild(j).v > graph.get(i).getChild(k).v + graph.get(k).getChild(j).v) {
                            graph.get(i).getChild(j).v = graph.get(i).getChild(k).v + graph.get(k).getChild(j).v;
                        }
                    }
                }
            }
        }

        /**
         * 2点間の距離
         *
         * @param from
         * @param to
         * @return
         */
        public long getDistance(long from, long to) {
            return graph.get(from).getChild(to).v;
        }

    }

    public long calcSimpleCombination(long n, long m, long CONST_MOD) {
        long mole = 1;
        for (long i = 1; i <= n + m; i++) {
            mole *= i;
            mole %= CONST_MOD;
        }
        long deno = 1;
        for (long i = 1; i <= n; i++) {
            deno *= i;
            deno %= CONST_MOD;
        }
        for (int i = 1; i <= m; i++) {
            deno *= i;
            deno %= CONST_MOD;
        }
        deno = modInverse(deno, CONST_MOD);
        return (mole * deno) % CONST_MOD;
    }

    long abs(double x) {
        return (long) Math.abs(x);
    }

    long round(double x) {
        return Math.round(x);
    }

    long floor(double x) {
        return (long) Math.floor(x);
    }

    long ceil(double x) {
        return (long) Math.ceil(x);
    }

    double sqrt(double x) {
        return Math.sqrt(x);
    }

    double pow(double x, double y) {
        return Math.pow(x, y);
    }

    long pow(long x, long y) {
        return (long) Math.pow(x, y);
    }

    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long gcd(long a, long b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long lcm(long a, long b) {
        return a * b / gcd(a, b);
    }

    public long lcmMod(long... ab) {

        Map<Long, Long> ps = new HashMap<Long, Long>();

        for (int abl = 0; abl < ab.length; abl++) {
            long target = ab[abl];
            long l = target;
            for (long p = 2; p * p <= l; p++) {
                long cnt = 0;
                while (target > 1 && target % p == 0) {
                    cnt++;
                    target /= p;
                }
                if (cnt == 0)
                    continue;
                ps.put(p, Long.max(cnt, ps.getOrDefault(p, 0L)));
            }
            if (target > 1)
                ps.put(target, Long.max(1, ps.getOrDefault(target, 0L)));
        }
        long res = 1L;
        for (Map.Entry<Long, Long> e : ps.entrySet()) {
            res *= powMod(e.getKey(), e.getValue());
            res %= MOD;
        }
        return res;
    }

    int upperToInt(char a) {
        return a - 'A';
    }

    int lowerToInt(char a) {
        return a - 'a';
    }

    int numToInt(char a) {
        return a - '0';
    }

    int charToInt(char a) {
        return a >= 'a' ? lowerToInt(a) : a >= 'A' ? upperToInt(a) : numToInt(a);
    }

    char intToUpper(int a) {
        return (char) (a + 'A');
    }

    char intToLower(int a) {
        return (char) (a + 'a');
    }

    char intToNum(int a) {
        return (char) (a + '0');
    }

    void reverse(String array[]) {
        String reversed[] = new String[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(int array[]) {
        int reversed[] = new int[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(long array[]) {
        long reversed[] = new long[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(double array[]) {
        double reversed[] = new double[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void reverse(boolean array[]) {
        boolean reversed[] = new boolean[array.length];
        for (int i = 0; i < array.length; i++) {
            reversed[array.length - i - 1] = array[i];
        }
        for (int i = 0; i < array.length; i++) {
            array[i] = reversed[i];
        }
    }

    void fill(int array[][], int x) {
        for (int a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(long array[][], long x) {
        for (long a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(double array[][], double x) {
        for (double a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(boolean array[][], boolean x) {
        for (boolean a[] : array) {
            Arrays.fill(a, x);
        }
    }

    void fill(int array[][][], int x) {
        for (int a[][] : array) {
            fill(a, x);
        }
    }

    void fill(long array[][][], long x) {
        for (long a[][] : array) {
            fill(a, x);
        }
    }

    void fill(double array[][][], double x) {
        for (double a[][] : array) {
            fill(a, x);
        }
    }

    void fill(boolean array[][][], boolean x) {
        for (boolean a[][] : array) {
            fill(a, x);
        }
    }

    long L_INF = (long) 1e18 + 7;

    boolean isINF(long a) {
        return abs(a) > L_INF / 1000;
    }

    boolean isPlusINF(long a) {
        return a > 0 && isINF(a);
    }

    boolean isMinusINF(long a) {
        return isPlusINF(-a);
    }

    int I_INF = (int) 1e9 + 7;

    boolean isINF(int a) {
        return abs(a) > I_INF / 1000;
    }

    boolean isPlusINF(int a) {
        return a > 0 && isINF(a);
    }

    boolean isMinusINF(int a) {
        return isPlusINF(-a);
    }

    /**
     * 指定したx以下の素数をリストアップする
     */
    public long[] getPrimesUnderX(long x) {
        return LongStream.rangeClosed(2, x)
                .filter(i -> LongStream.rangeClosed(2, (long) Math.sqrt(i)).allMatch(j -> i % j != 0)).toArray();
    }


    public long mod(long i) {
        return i % MOD + ((i % MOD) < 0 ? MOD : 0);
    }

    long powMod(long x, long y) {
        if (y == 0) {
            return 1;
        } else {
            long tmp = powMod(x, y / 2);
            return mod(mod(tmp * tmp) * (y % 2 == 0 ? 1 : x));
        }
    }

    long inv(long x) {
        return powMod(x, MOD - 2);
    }

    int MAX_FACT = 5_000_100;
    long fact[];
    long invFact[];

    /**
     * Combination簡易版
     * 5 C 2
     * 異なる n個のものから r個を選ぶ組み合わせの総数 nCr を求めます。
     * 5!(5*4*3*2*1)
     * /
     * 2!(2*1) *  (5-2)!(3*2*1)
     *
     * @param n
     * @param r
     * @return
     */
    private long getComb(int n, int r) {
        long tmp = 1;
        for (int i = 1; i <= r; i++) {
            tmp *= n - i + 1;
            tmp = mod(tmp);
            tmp *= inv(i);
            tmp = mod(tmp);
        }
        return tmp;
    }

    /**
     * 階乗計算の事前累積和
     * [1, 1, 2, 3, 4, 5, … FACTORIAL_NUM]
     * mod済
     */
    void prepareFact() {
        fact = new long[MAX_FACT];
        Arrays.fill(fact, 0);
        invFact = new long[MAX_FACT];
        Arrays.fill(invFact, 0);
        fact[0] = 1;
        int maxIndex = (int) min(MAX_FACT, (int) MOD);
        for (int i = 1; i < maxIndex; i++) {
            fact[i] = mod(fact[i - 1] * i);
        }
        invFact[maxIndex - 1] = inv(fact[maxIndex - 1]);
        for (int i = maxIndex - 1; i > 0; i--) {
            invFact[i - 1] = mod(invFact[i] * i);
        }
    }

    /**
     * 順列
     * nPk -> n! / (n-k)!
     *
     * @param n
     * @param r
     * @return
     */
    long permutation(int n, int r) {
        if (n < 0 || r < 0 || n < r) {
            return 0;
        }
        return mod(fact[n] * invFact[n - r]);
    }

    /**
     * 組み合わせ
     * nCk -> n! / k!・(n-k)!
     *
     * @param n
     * @param r
     * @return
     */
    long combination(int n, int r) {
        if (n < 0 || r < 0 || n < r) {
            return 0;
        }
        return mod(permutation(n, r) * invFact[r]);
    }

    /**
     * 重複組合せ nHr （同次積）
     * nHr = (n+r-1)Cr
     * 異なるn個のものから重複を許してr個取る組合せの総数
     * 例：
     * リンゴ，ミカン，牛肉の3種類の果物があります．これらの中から6個の食材を買って帰ります．
     * このとき，何通りの買い方がありますか？ただし，含まれない食材があってもよいものとします
     *
     * @param n
     * @param r
     * @return
     */
    long homogeneousProduct(int n, int r) {
        return combination((n - 1) + r, r);
    }

    /**
     * 多項係数
     * 文字aをp個,bをq個,cをr個, dをs個 あわせてn個を1列に並べるときの並べ方
     * n! / p!・q!・r!・s!
     *
     * @param n
     * @param strNum
     * @param mod
     * @return
     */

    /**
     * フェルマーの小定理を用いて逆元を求める。
     * ある数xのmod p（pは素数）の逆数x'はx' = x^(p-2)
     * 繰り返し二乗法を用いて計算する。
     * http://satanic0258.hatenablog.com/entry/2016/04/29/004730
     * {@link BigInteger#modInverse(BigInteger)}とどちらが速いか？
     *
     * @param x
     * @return
     */
    private long modInverse(long x, long mod) {
        long res = 1L;
        long k = mod - 2L;
        long y = x;
        while (k != 0) {
            if (k % 2 != 0) {
                res = (res * y) % mod;
            }
            y = (y * y) % mod;
            k /= 2;
        }
        return res;
    }

    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private static boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    private void skipUnprintable() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
    }

    public boolean hasNext() {
        skipUnprintable();
        return hasNextByte();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public long min(long... v) {
        long min = Long.MAX_VALUE;
        for (long i : v) min = Math.min(min, i);
        return min;
    }

    public long max(long... v) {
        long max = Long.MIN_VALUE;
        for (long i : v) max = Math.max(max, i);
        return max;
    }
}