Polycarp invited all his friends to the tea party to celebrate the holiday. He has n cups, one for each of his n friends, with volumes a1, a2, ..., an. His teapot stores w milliliters of tea (w ≤ a1 + a2 + ... + an). Polycarp wants to pour tea in cups in such a way that:

  * Every cup will contain tea for at least half of its volume 
  * Every cup will contain integer number of milliliters of tea 
  * All the tea from the teapot will be poured into cups 
  * All friends will be satisfied. 



Friend with cup i won't be satisfied, if there exists such cup j that cup i contains less tea than cup j but ai > aj.

For each cup output how many milliliters of tea should be poured in it. If it's impossible to pour all the tea and satisfy all conditions then output -1.

Input

The first line contains two integer numbers n and w (1 ≤ n ≤ 100, <image>).

The second line contains n numbers a1, a2, ..., an (1 ≤ ai ≤ 100).

Output

Output how many milliliters of tea every cup should contain. If there are multiple answers, print any of them.

If it's impossible to pour all the tea and satisfy all conditions then output -1.

Examples

Input

2 10
8 7


Output

6 4 


Input

4 4
1 1 1 1


Output

1 1 1 1 


Input

3 10
9 8 10


Output

-1

Note

In the third example you should pour to the first cup at least 5 milliliters, to the second one at least 4, to the third one at least 5. It sums up to 14, which is greater than 10 milliliters available.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.io.FileReader;
import java.util.Comparator;
import java.io.InputStream;

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

    static class TaskC {
        public void solve(int testNumber, Scanner sc, PrintWriter out) {
            int n = sc.nextInt();
            int w = sc.nextInt();
            TaskC.Pair[] pairs = new TaskC.Pair[n];
            int totalHalf = 0;
            for (int i = 0; i < n; i++) {
                int vol = sc.nextInt();
                pairs[i] = new TaskC.Pair(vol, i);
                totalHalf += (vol + 1) / 2;
            }

            if (totalHalf > w) {
                out.println(-1);
                return;
            }
            int[] res = new int[n];
            Arrays.sort(pairs, new Comparator<TaskC.Pair>() {

                public int compare(TaskC.Pair pair, TaskC.Pair t1) {
                    return t1.vol - pair.vol;
                }
            });
            for (int i = 0; i < n; i++)
                res[pairs[i].idx] = (pairs[i].vol + 1) / 2;

            int rem = w - totalHalf;
            for (int i = 0; i < n; i++) {
                int add = Math.min(rem, pairs[i].vol - res[pairs[i].idx]);
                rem -= add;
                res[pairs[i].idx] += add;
            }

            for (int i = 0; i < n; i++) {
                if (i > 0) out.print(" ");
                out.print(res[i]);
            }
            out.println();
        }

        static class Pair {
            int vol;
            int idx;

            Pair(int v, int i) {
                vol = v;
                idx = i;
            }

        }

    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader f) {
            br = new BufferedReader(f);
        }

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

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

    }
}

