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.awt.Point;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.text.DecimalFormat;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

public class Main {
    static Main.MyScanner sc = new Main.MyScanner();
    // static Main.Parser sc = new Parser(System.in);
    static PrintWriter out = new PrintWriter(System.out, true);

    public static void main(String[] args) throws Exception {
        int n = sc.nextInt(),doneTests = sc.nextInt(), maxMarks = sc.nextInt(),maxSum = sc.nextInt(),minMedian = sc.nextInt(),ip[] = new int[doneTests];
        long sum = 0 ;
        for(int i = 0 ; i < doneTests ; i++)
            ip[i] = sc.nextInt() ;
        Arrays.sort(ip);
        ArrayList<Integer> al = new ArrayList<Integer>(n) ;
        for(int i = 0 ; i < doneTests ; i++){
            al.add(ip[i]) ;
            sum += ip[i];
        }
        boolean flag = true ;
        Collections.sort(al);
//      System.out.println(al);
        while(al.size() != n){
            if(al.size() == 0 || al.get((al.size()-1)/2) < minMedian ){
                sum += minMedian ;
                al.add(minMedian) ;
            }else{
                sum++;
                al.add(1);
            }
            Collections.sort(al);
//          System.out.println(al);
        }
        if(sum <= maxSum && al.get(n/2) >= minMedian)
            for(int i = 0,pos = 0 ; i < al.size() ; i++){
                if(pos < ip.length && al.get(i) == ip[pos]){
                    pos++;
                }else{
                    out.print(al.get(i)+" ");
                }
            }
        else
            out.print(-1);
        out.println();  
        
        out.close();
    }
    

    static private class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public int mod(long x) {
            return (int) x % 1000000007;
        }

        public int mod(int x) {
            return x % 1000000007;
        }

        boolean hasNext() {
            if (st.hasMoreElements())
                return true;
            try {
                st = new StringTokenizer(br.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
            return st.hasMoreTokens();
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

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

    static class Parser {
        final private int BUFFER_SIZE = 65536; // 2^16, a good compromise for
                                                // some problems
        private InputStream din; // Underlying input stream
        private byte[] buffer; // Self-maintained buffer
        private int bufferPointer; // Current read position in the buffer
        private int bytesRead; // Effective bytes in the buffer read from the
                                // input stream

        public Parser(InputStream in) {
            din = in;
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        /**
         * Read the next integer from the input stream.
         * 
         * @return The next integer.
         * @throws IOException
         */
        public int nextInt() throws IOException {
            int result = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            while (c >= '0' && c <= '9') {
                result = result * 10 + c - '0';
                c = read();
            }
            if (neg)
                return -result;
            return result;
        }

        /**
         * Read the next byte of data from the input stream.
         * 
         * @return the next byte of data, or -1 if the end of the stream is
         *         reached.
         * @throws IOException
         *             if an I/O error occurs.
         */
        public byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        /**
         * Read data from the input stream into the buffer
         * 
         * @throws IOException
         *             if an I/O error occurs.
         */
        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
    }
}