Problem: Little Vova studies programming in an elite school. Vova and his classmates are supposed to write n progress tests, for each test they will get a mark from 1 to p. Vova is very smart and he can write every test for any mark, but he doesn't want to stand out from the crowd too much. If the sum of his marks for all tests exceeds value x, then his classmates notice how smart he is and start distracting him asking to let them copy his homework. And if the median of his marks will be lower than y points (the definition of a median is given in the notes), then his mom will decide that he gets too many bad marks and forbid him to play computer games.

Vova has already wrote k tests and got marks a1, ..., ak. He doesn't want to get into the first or the second situation described above and now he needs to determine which marks he needs to get for the remaining tests. Help him do that.

Input

The first line contains 5 space-separated integers: n, k, p, x and y (1 ≤ n ≤ 999, n is odd, 0 ≤ k < n, 1 ≤ p ≤ 1000, n ≤ x ≤ n·p, 1 ≤ y ≤ p). Here n is the number of tests that Vova is planned to write, k is the number of tests he has already written, p is the maximum possible mark for a test, x is the maximum total number of points so that the classmates don't yet disturb Vova, y is the minimum median point so that mom still lets him play computer games.

The second line contains k space-separated integers: a1, ..., ak (1 ≤ ai ≤ p) — the marks that Vova got for the tests he has already written.

Output

If Vova cannot achieve the desired result, print "-1".

Otherwise, print n - k space-separated integers — the marks that Vova should get for the remaining tests. If there are multiple possible solutions, print any of them.

Examples

Input

5 3 5 18 4
3 5 4


Output

4 1


Input

5 3 5 16 4
5 5 5


Output

-1

Note

The median of sequence a1, ..., an where n is odd (in this problem n is always odd) is the element staying on (n + 1) / 2 position in the sorted list of ai.

In the first sample the sum of marks equals 3 + 5 + 4 + 4 + 1 = 17, what doesn't exceed 18, that means that Vova won't be disturbed by his classmates. And the median point of the sequence {1, 3, 4, 4, 5} equals to 4, that isn't less than 4, so his mom lets him play computer games.

Please note that you do not have to maximize the sum of marks or the median mark. Any of the answers: "4 2", "2 4", "5 1", "1 5", "4 1", "1 4" for the first test is correct.

In the second sample Vova got three '5' marks, so even if he gets two '1' marks, the sum of marks will be 17, that is more than the required value of 16. So, the answer to this test is "-1".

Solution (in JAVA):

Solution:
import java.io.*;
import java.math.*;
import java.util.*;

public class Main {
    public static void main (String[] args) {
        FastReader in = new FastReader(System.in);

        int n = in.nextInt(), k = in.nextInt(), p = in.nextInt(), x = in.nextInt(), y = in.nextInt();
        int[] a = in.nextIntArray(k);
        Arrays.sort(a);

        int sum = 0;
        for (int i = 0; i < a.length; i++) {
            sum += a[i];
        }
        int min = -1; for (int i = 0; i < a.length; i++) { if (a[i] >= y) { min = i; break; } }

        if (k >= (n + 1)/ 2 && a[n / 2] < y) {
            System.out.println(-1);
            return;
        }

        int vi;
        int vs;
        if (min != -1) {
            vi = Math.min(n - k, (n + 1) / 2 - 1 - min);
        } else {
            vi = Math.max(0, n / 2 - k);
        }
        vs = n - k - vi;

        //System.out.println(vi + " " + vs);
        sum += vi + vs * y;
        if (sum > x) {
            System.out.println(-1);
            return;
        }

        for (int i = 0; i < vi; i++) {
            System.out.print(1 + " ");
        }
        for (int i = 0; i < vs; i++) {
            System.out.print(y + " ");
        }
    }
}

class FastReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public FastReader(InputStream stream) {
        this.reader = new BufferedReader(new InputStreamReader(stream));
        this.tokenizer = new StringTokenizer("");
    }

    public boolean hasNext() {
        return ensureTokens();
    }

    public String next() {
        return  ensureTokens() ? tokenizer.nextToken() : null;
    }

    private boolean ensureTokens() {
        while(!tokenizer.hasMoreTokens()){
            try{
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (Exception e){
                return false;
            }
        }
        return true;
    }

    public String nextLine() {
        try {
            return reader.readLine();
        } catch (Exception e) {
            return null;
        }
    }

    public char[] nextCharArray() {
        return nextLine().toCharArray();
    }

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

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

    public int[] nextIntArrayOnLine() {
        String line = nextLine();
        String[] tokens = line.split(" ");
        int[] array = new int[tokens.length];
        for (int i = 0; i < tokens.length; i++) {
            array[i] = Integer.parseInt(tokens[i]);
        }
        return array;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextLong();
        }
        return array;
    }

    public float nextFloat() {
        return Float.parseFloat(next());
    }

    public float[] nextFloatArray(int size) {
        float[] array = new float[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextFloat();
        }
        return array;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextDouble();
        }
        return array;
    }

    public short nextShort() {
        return Short.parseShort(next());
    }

    public short[] nextShortArray(int size) {
        short[] array = new short[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextShort();
        }
        return array;
    }

    public BigDecimal nextBigDecimal() {
        return new BigDecimal(next());
    }

    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
}

class FastWriter {
    private final PrintWriter printWriter;

    public FastWriter(OutputStream stream) {
        printWriter = new PrintWriter(new BufferedWriter(new OutputStreamWriter(stream)));
    }

    public FastWriter(Writer writer) {
        printWriter = new PrintWriter(writer);
    }

    public void close() {
        printWriter.close();
    }

    public void print(boolean element) {
        printWriter.print(element);
    }

    public void print(char[] element) {
        printWriter.print(element);
    }

    public void print(double element) {
        printWriter.print(element);
    }

    public void print(float element) {
        printWriter.print(element);
    }

    public void print(int element) {
        printWriter.print(element);
    }

    public void print(long element) {
        printWriter.print(element);
    }

    public void print(String element) {
        printWriter.print(element);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                printWriter.print(' ');
            }
            printWriter.print(objects[i]);
        }
    }

    public void println(boolean element) {
        printWriter.println(element);
    }

    public void println(char[] element) {
        printWriter.println(element);
    }

    public void println(double element) {
        printWriter.println(element);
    }

    public void println(float element) {
        printWriter.println(element);
    }

    public void println(int element) {
        printWriter.println(element);
    }

    public void println(long element) {
        printWriter.println(element);
    }

    public void println(String element) {
        printWriter.println(element);
    }

    public void println() {
        printWriter.println();
    }

    public void println(Object... objects) {
        print(objects);
        printWriter.println();
    }

    public void printf(String format, Object... args) {
        printWriter.printf(format, args);
    }
}