Problem: Once Bob decided to lay a parquet floor in his living room. The living room is of size n × m metres. Bob had planks of three types: a planks 1 × 2 meters, b planks 2 × 1 meters, and c planks 2 × 2 meters. Help Bob find out, if it is possible to parquet the living room with such a set of planks, and if it is possible, find one of the possible ways to do so. Bob doesn't have to use all the planks.

Input

The first input line contains 5 space-separated integer numbers n, m, a, b, c (1 ≤ n, m ≤ 100, 0 ≤ a, b, c ≤ 104), n and m — the living room dimensions, a, b and c — amount of planks 1 × 2, 2 × 1 и 2 × 2 respectively. It's not allowed to turn the planks.

Output

If it is not possible to parquet the room with such a set of planks, output IMPOSSIBLE. Otherwise output one of the possible ways to parquet the room — output n lines with m lower-case Latin letters each. Two squares with common sides should contain the same letters, if they belong to one and the same plank, and different letters otherwise. Different planks can be marked with one and the same letter (see examples). If the answer is not unique, output any.

Examples

Input

2 6 2 2 1


Output

aabcca
aabdda


Input

1 1 100 100 100


Output

IMPOSSIBLE


Input

4 4 10 10 10


Output

aabb
aabb
bbaa
bbaa

Solution (in JAVA):

Solution:
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

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

class Parquet {
    public void solve(int testNumber, PandaScanner in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int a = in.nextInt();
        int b = in.nextInt();
        int c = in.nextInt();
        if (((n * m) & 1) > 0) {
            out.println("IMPOSSIBLE");
            return;
        }
        char[][] board = new char[n][m];
        int sX = 0;
        int sY = 0;
        if ((n & 1) > 0) {
            int curr = 0;
            for (int i = 0; i < m; i += 2) {
                board[0][i] = board[0][i + 1] = (char) (curr + 'a');
                curr ^= 1;
            }
            a -= m >> 1;
            sX++;
        }
        if ((m & 1) > 0) {
            int curr = 0;
            for (int i = 0; i < n; i += 2) {
                board[i][0] = board[i + 1][0] = (char) (curr + 'a');
                curr ^= 1;
            }
            b -= n >> 1;
            sY++;
        }
        if (a < 0 || b < 0 || (a / 2 + b / 2 + c < (n / 2) * (m / 2))) {
            out.println("IMPOSSIBLE");
            return;
        }
        int currIdx[] = new int[2];
        int currRow = 0;
        for (int i = sX; i < n; i += 2) {
            for (int j = sY; j < m; j+= 2) {
                if (c > 0) {
                    char toPaint = (char) (2 + currRow * 8 + currIdx[currRow] + 'a');
                    board[i][j] = board[i][j + 1] = board[i + 1][j] = board[i + 1][j + 1] = toPaint;
                    currIdx[currRow] = (currIdx[currRow] + 1) & 7;
                    c--;
                }
                else if (b > 1) {
                    char toPaint = (char) (2 + currRow * 8 + currIdx[currRow] + 'a');
                    board[i][j] = board[i + 1][j] = toPaint;
                    currIdx[currRow] = (currIdx[currRow] + 1) & 7;
                    toPaint = (char) (2 + currRow * 8 + currIdx[currRow] + 'a');
                    board[i][j + 1] = board[i + 1][j + 1] = toPaint;
                    currIdx[currRow] = (currIdx[currRow] + 1) & 7;
                    b -= 2;
                }
                else if (a > 1) {
                    char toPaint = (char) (2 + currRow * 8 + currIdx[currRow] + 'a');
                    board[i][j] = board[i][j + 1] = toPaint;
                    currIdx[currRow] = (currIdx[currRow] + 1) & 7;
                    toPaint = (char) (2 + currRow * 8 + currIdx[currRow] + 'a');
                    board[i + 1][j] = board[i + 1][j + 1] = toPaint;
                    currIdx[currRow] = (currIdx[currRow] + 1) & 7;
                    a -= 2;
                }
            }
            currRow ^= 1;
        }
        for (int i = 0; i < n; i++) {
            out.println(new String(board[i]));
        }
    }
}

class PandaScanner {
    public BufferedReader br;
    public StringTokenizer st;
    public InputStream in;

    public PandaScanner(InputStream in) {
        br = new BufferedReader(new InputStreamReader(this.in = in));
    }

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

    public String next() {
        if (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(nextLine().trim());
            return next();
        }
        return st.nextToken();
    }

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

    }