Problem: Anya loves to fold and stick. Today she decided to do just that.

Anya has n cubes lying in a line and numbered from 1 to n from left to right, with natural numbers written on them. She also has k stickers with exclamation marks. We know that the number of stickers does not exceed the number of cubes.

Anya can stick an exclamation mark on the cube and get the factorial of the number written on the cube. For example, if a cube reads 5, then after the sticking it reads 5!, which equals 120.

You need to help Anya count how many ways there are to choose some of the cubes and stick on some of the chosen cubes at most k exclamation marks so that the sum of the numbers written on the chosen cubes after the sticking becomes equal to S. Anya can stick at most one exclamation mark on each cube. Can you do it?

Two ways are considered the same if they have the same set of chosen cubes and the same set of cubes with exclamation marks.

Input

The first line of the input contains three space-separated integers n, k and S (1 ≤ n ≤ 25, 0 ≤ k ≤ n, 1 ≤ S ≤ 1016) — the number of cubes and the number of stickers that Anya has, and the sum that she needs to get. 

The second line contains n positive integers ai (1 ≤ ai ≤ 109) — the numbers, written on the cubes. The cubes in the input are described in the order from left to right, starting from the first one. 

Multiple cubes can contain the same numbers.

Output

Output the number of ways to choose some number of cubes and stick exclamation marks on some of them so that the sum of the numbers became equal to the given number S.

Examples

Input

2 2 30
4 3


Output

1


Input

2 2 7
4 3


Output

1


Input

3 1 1
1 1 1


Output

6

Note

In the first sample the only way is to choose both cubes and stick an exclamation mark on each of them.

In the second sample the only way is to choose both cubes but don't stick an exclamation mark on any of them.

In the third sample it is possible to choose any of the cubes in three ways, and also we may choose to stick or not to stick the exclamation mark on it. So, the total number of ways is six.

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Iterator;
import java.util.AbstractSet;
import java.util.Set;
import java.util.InputMismatchException;
import java.io.IOException;
import java.util.Random;
import java.util.AbstractMap;
import java.util.Map;
import java.util.Map.Entry;
import java.util.NoSuchElementException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Pradyumn
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        FastReader in = new FastReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskE solver = new TaskE();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskE {
        static long[] factorials = new long[19];

        static {
            factorials[0] = 1;
            for (int i = 1; i <= 18; ++i) factorials[i] = factorials[i - 1] * (1L) * i;
        }

        public void solve(int testNumber, FastReader in, PrintWriter out) {
            int n = in.nextInt();
            int k = in.nextInt();
            long S = in.nextLong();
            int[] a = in.nextIntArray(n);
            long[] facs = new long[n];
            for (int i = 0; i < n; ++i) {
                if (a[i] <= 18) {
                    facs[i] = factorials[a[i]];
                }
            }
            int[] half1 = Arrays.copyOfRange(a, 0, n >> 1);
            int[] half2 = Arrays.copyOfRange(a, n >> 1, n);

            TaskE.CountMap[] maps1 = compute(half1);
            TaskE.CountMap[] maps2 = compute(half2);

            long sum = 0;
            for (int i = 0; i < maps1.length; i++) {
                for (int j = 0; j < maps2.length && i + j <= k; j++) {
                    for (Map.Entry<Long, Long> kvp : maps1[i].entrySet()) {
                        long K = kvp.getKey();
                        long v = kvp.getValue();
                        long target = S - K;
                        sum += v * maps2[j].getValue(target);
                    }
                }
            }
            out.println(sum);
        }

        public static TaskE.CountMap[] compute(int[] a) {
            int n = a.length;
            long[] facs = new long[n];
            for (int i = 0; i < n; ++i) {
                if (a[i] <= 18) {
                    facs[i] = factorials[a[i]];
                }
            }
            TaskE.CountMap[] maps = new TaskE.CountMap[n + 2];
            for (int i = 0; i < maps.length; ++i) {
                maps[i] = new TaskE.CountMap();
            }
            maps[0].put(0L, 1L);
            for (int i = 0; i < n; i++) {
                TaskE.CountMap[] adds = new TaskE.CountMap[i + 2];
                for (int j = 0; j <= i + 1; j++) {
                    adds[j] = new TaskE.CountMap();
                }
                for (int j = 0; j <= i; j++) {
                    for (Map.Entry<Long, Long> kvp : maps[j].entrySet()) {
                        long k = kvp.getKey();
                        long v = kvp.getValue();
                        adds[j].addValue(k + a[i], v);
                    }
                }
                if (facs[i] > 0) {
                    for (int j = 0; j <= i; j++) {
                        for (Map.Entry<Long, Long> kvp : maps[j].entrySet()) {
                            long k = kvp.getKey();
                            long v = kvp.getValue();
                            adds[j + 1].addValue(k + facs[i], v);
                        }
                    }
                }
                for (int j = 0; j <= i + 1; j++) {
                    maps[j].mergeAdd(adds[j]);
                }
            }
            return maps;
        }

        public static class CountMap extends EHashMap<Long, Long> {
            public long getValue(Long key) {
                return this.containsKey(key) ? this.get(key) : 0L;
            }

            public void addValue(long key, long value) {
                this.put(key, this.getValue(key) + value);
            }

            public void mergeAdd(TaskE.CountMap cm) {
                for (Map.Entry<Long, Long> kvp : cm.entrySet()) {
                    long k = kvp.getKey();
                    long v = kvp.getValue();
                    this.addValue(k, v);
                }
            }

        }

    }

    static class FastReader {
        private InputStream stream;
        private byte[] buf = new byte[8192];
        private int curChar;
        private int pnumChars;
        private FastReader.SpaceCharFilter filter;

        public FastReader(InputStream stream) {
            this.stream = stream;
        }

        private int pread() {
            if (pnumChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= pnumChars) {
                curChar = 0;
                try {
                    pnumChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (pnumChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            int res = 0;
            do {
                if (c == ',') {
                    c = pread();
                }
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int[] array = new int[n];
            for (int i = 0; i < n; i++) {
                array[i] = nextInt();
            }
            return array;
        }

        public long nextLong() {
            int c = pread();
            while (isSpaceChar(c))
                c = pread();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = pread();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = pread();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        private boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

        private static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }

    static class EHashMap<E, V> extends AbstractMap<E, V> {
        private final int[] shifts = new int[10];
        private int size;
        private HashEntry<E, V>[] data;
        private int capacity;
        private Set<Entry<E, V>> entrySet;

        {
            Random random = new Random(System.currentTimeMillis());
            for (int i = 0; i < 10; i++) {
                shifts[i] = 1 + 3 * i + random.nextInt(3);
            }
        }

        public EHashMap() {
            this(4);
        }

        private void setCapacity(int size) {
            capacity = Integer.highestOneBit(4 * size);
            data = new HashEntry[capacity];
        }

        public EHashMap(int maxSize) {
            setCapacity(maxSize);
            entrySet = new AbstractSet<Entry<E, V>>() {

                public Iterator<Entry<E, V>> iterator() {
                    return new Iterator<Entry<E, V>>() {
                        private HashEntry<E, V> last = null;
                        private HashEntry<E, V> current = null;
                        private HashEntry<E, V> base = null;
                        private int lastIndex = -1;
                        private int index = -1;

                        public boolean hasNext() {
                            if (current == null) {
                                for (index++; index < capacity; index++) {
                                    if (data[index] != null) {
                                        base = current = data[index];
                                        break;
                                    }
                                }
                            }
                            return current != null;
                        }

                        public Entry<E, V> next() {
                            if (!hasNext()) {
                                throw new NoSuchElementException();
                            }
                            last = current;
                            lastIndex = index;
                            current = current.next;
                            if (base.next != last) {
                                base = base.next;
                            }
                            return last;
                        }

                        public void remove() {
                            if (last == null) {
                                throw new IllegalStateException();
                            }
                            size--;
                            if (base == last) {
                                data[lastIndex] = last.next;
                            } else {
                                base.next = last.next;
                            }
                        }
                    };
                }


                public int size() {
                    return size;
                }
            };
        }

        public EHashMap(Map<E, V> map) {
            this(map.size());
            putAll(map);
        }


        public Set<Entry<E, V>> entrySet() {
            return entrySet;
        }


        public void clear() {
            Arrays.fill(data, null);
            size = 0;
        }

        private int index(Object o) {
            return getHash(o.hashCode()) & (capacity - 1);
        }

        private int getHash(int h) {
            int result = h;
            for (int i : shifts) {
                result ^= h >>> i;
            }
            return result;
        }


        public V remove(Object o) {
            if (o == null) {
                return null;
            }
            int index = index(o);
            HashEntry<E, V> current = data[index];
            HashEntry<E, V> last = null;
            while (current != null) {
                if (current.key.equals(o)) {
                    if (last == null) {
                        data[index] = current.next;
                    } else {
                        last.next = current.next;
                    }
                    size--;
                    return current.value;
                }
                last = current;
                current = current.next;
            }
            return null;
        }


        public V put(E e, V value) {
            if (e == null) {
                return null;
            }
            int index = index(e);
            HashEntry<E, V> current = data[index];
            if (current != null) {
                while (true) {
                    if (current.key.equals(e)) {
                        V oldValue = current.value;
                        current.value = value;
                        return oldValue;
                    }
                    if (current.next == null) {
                        break;
                    }
                    current = current.next;
                }
            }
            if (current == null) {
                data[index] = new HashEntry<E, V>(e, value);
            } else {
                current.next = new HashEntry<E, V>(e, value);
            }
            size++;
            if (2 * size > capacity) {
                HashEntry<E, V>[] oldData = data;
                setCapacity(size);
                for (HashEntry<E, V> entry : oldData) {
                    while (entry != null) {
                        HashEntry<E, V> next = entry.next;
                        index = index(entry.key);
                        entry.next = data[index];
                        data[index] = entry;
                        entry = next;
                    }
                }
            }
            return null;
        }


        public V get(Object o) {
            if (o == null) {
                return null;
            }
            int index = index(o);
            HashEntry<E, V> current = data[index];
            while (current != null) {
                if (current.key.equals(o)) {
                    return current.value;
                }
                current = current.next;
            }
            return null;
        }


        public boolean containsKey(Object o) {
            if (o == null) {
                return false;
            }
            int index = index(o);
            HashEntry<E, V> current = data[index];
            while (current != null) {
                if (current.key.equals(o)) {
                    return true;
                }
                current = current.next;
            }
            return false;
        }


        public int size() {
            return size;
        }

        private class HashEntry<E, V> implements Entry<E, V> {
            private final E key;
            private V value;
            private HashEntry<E, V> next;

            private HashEntry(E key, V value) {
                this.key = key;
                this.value = value;
            }

            public E getKey() {
                return key;
            }

            public V getValue() {
                return value;
            }

            public V setValue(V value) {
                V oldValue = this.value;
                this.value = value;
                return oldValue;
            }

        }

    }
}