Problem: Given are N pairwise distinct non-negative integers A_1,A_2,\ldots,A_N. Find the number of ways to choose a set of between 1 and K numbers (inclusive) from the given numbers so that the following two conditions are satisfied:

* The bitwise AND of the chosen numbers is S.
* The bitwise OR of the chosen numbers is T.

Constraints

* 1 \leq N \leq 50
* 1 \leq K \leq N
* 0 \leq A_i < 2^{18}
* 0 \leq S < 2^{18}
* 0 \leq T < 2^{18}
* A_i \neq A_j (1 \leq i < j \leq N)

Input

Input is given from Standard Input in the following format:


N K S T
A_1 A_2 ... A_N


Output

Print the answer.

Examples

Input

3 3 0 3
1 2 3


Output

2


Input

5 3 1 7
3 4 9 1 5


Output

2


Input

5 4 0 15
3 4 9 1 5


Output

3

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.PrintStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            EOrand solver = new EOrand();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class EOrand {
        Debug debug = new Debug(false);
        int k;
        long[][] comb = new long[100][100];
        int[] a;

        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            k = in.readInt();
            int s = in.readInt();
            int t = in.readInt();
            IntegerList list = new IntegerList(n);
            for (int i = 0; i < n; i++) {
                int x = in.readInt();
                if ((x & s) != s || (x | t) != t) {
                    continue;
                }
                list.add(x);
            }

            a = list.toArray();
            n = a.length;

            SequenceUtils.deepFill(comb, -1L);

            int[] clone = a.clone();
            int mask = (1 << 18) - 1;

            long ans = 0;
            for (int i = 0; i < n; i++) {
                int reqOne = t - clone[i];
                int reqZero = (clone[i]) & (mask ^ s);
                int req = reqOne | reqZero;

                a = Arrays.copyOfRange(clone, i + 1, clone.length);
                for (int j = 0; j < a.length; j++) {
                    a[j] = (a[j] & reqOne) | (~a[j] & reqZero);
                }

                long local = 0;
                SubsetGenerator sg = new SubsetGenerator();
                sg.reset(req);

                while (sg.hasNext()) {
                    int next = sg.next();
                    local += ie(next);
                }

                ans += local;
                debug.debug("local", local);
            }

            out.println(ans);
        }

        public long ie(int set) {
            int cnt = 0;
            for (int x : a) {
                if ((x & set) == 0) {
                    cnt++;
                }
            }
            long ans = 0;
            for (int j = 0, min = Math.min(k - 1, cnt); j <= min; j++) {
                ans += comb(cnt, j);
            }
            if (Integer.bitCount(set) % 2 == 1) {
                ans = -ans;
            }
            return ans;
        }

        public long comb(int n, int m) {
            if (comb[n][m] == -1) {
                if (m > n) {
                    return comb[n][m] = 0;
                }
                if (m == 0) {
                    return comb[n][m] = 1;
                }
                comb[n][m] = comb(n - 1, m) + comb(n - 1, m - 1);
            }
            return comb[n][m];
        }

    }

    static class IntegerList implements Cloneable {
        private int size;
        private int cap;
        private int[] data;
        private static final int[] EMPTY = new int[0];

        public IntegerList(int cap) {
            this.cap = cap;
            if (cap == 0) {
                data = EMPTY;
            } else {
                data = new int[cap];
            }
        }

        public IntegerList(IntegerList list) {
            this.size = list.size;
            this.cap = list.cap;
            this.data = Arrays.copyOf(list.data, size);
        }

        public IntegerList() {
            this(0);
        }

        public void ensureSpace(int req) {
            if (req > cap) {
                while (cap < req) {
                    cap = Math.max(cap + 10, 2 * cap);
                }
                data = Arrays.copyOf(data, cap);
            }
        }

        public void add(int x) {
            ensureSpace(size + 1);
            data[size++] = x;
        }

        public void addAll(int[] x, int offset, int len) {
            ensureSpace(size + len);
            System.arraycopy(x, offset, data, size, len);
            size += len;
        }

        public void addAll(IntegerList list) {
            addAll(list.data, 0, list.size);
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

        public String toString() {
            return Arrays.toString(toArray());
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof IntegerList)) {
                return false;
            }
            IntegerList other = (IntegerList) obj;
            return SequenceUtils.equal(data, 0, size - 1, other.data, 0, other.size - 1);
        }

        public int hashCode() {
            int h = 1;
            for (int i = 0; i < size; i++) {
                h = h * 31 + Integer.hashCode(data[i]);
            }
            return h;
        }

        public IntegerList clone() {
            IntegerList ans = new IntegerList();
            ans.addAll(this);
            return ans;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private StringBuilder cache = new StringBuilder(10 << 20);
        private final Writer os;

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput append(char c) {
            cache.append(c);
            return this;
        }

        public FastOutput append(long c) {
            cache.append(c);
            return this;
        }

        public FastOutput println(long c) {
            return append(c).println();
        }

        public FastOutput println() {
            cache.append(System.lineSeparator());
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                os.flush();
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    bufLen = -1;
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

    }

    static class Debug {
        private boolean offline;
        private PrintStream out = System.err;

        public Debug(boolean enable) {
            offline = enable && System.getSecurityManager() == null;
        }

        public Debug debug(String name, long x) {
            if (offline) {
                debug(name, "" + x);
            }
            return this;
        }

        public Debug debug(String name, String x) {
            if (offline) {
                out.printf("%s=%s", name, x);
                out.println();
            }
            return this;
        }

    }

    static class SubsetGenerator {
        private int m;
        private int x;

        public void reset(int m) {
            this.m = m;
            this.x = m + 1;
        }

        public boolean hasNext() {
            return x != 0;
        }

        public int next() {
            return x = (x - 1) & m;
        }

    }

    static class SequenceUtils {
        public static void deepFill(Object array, long val) {
            if (!array.getClass().isArray()) {
                throw new IllegalArgumentException();
            }
            if (array instanceof long[]) {
                long[] longArray = (long[]) array;
                Arrays.fill(longArray, val);
            } else {
                Object[] objArray = (Object[]) array;
                for (Object obj : objArray) {
                    deepFill(obj, val);
                }
            }
        }

        public static boolean equal(int[] a, int al, int ar, int[] b, int bl, int br) {
            if ((ar - al) != (br - bl)) {
                return false;
            }
            for (int i = al, j = bl; i <= ar; i++, j++) {
                if (a[i] != b[j]) {
                    return false;
                }
            }
            return true;
        }

    }
}