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.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileReader;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.*;

public class C implements Runnable {
	private boolean _ReadFromFile = false; //System.getProperty("ONLINE_JUDGE") == null;
	private boolean _WriteToFile = false;
	static final String TASK_ID = "in";
	static final String IN_FILE = TASK_ID + ".in";
	static final String OUT_FILE = TASK_ID + ".out";
	BufferedReader reader;
	StringTokenizer tokenizer;
	PrintWriter writer;
	private int hor;
	private int ver;
	private int square;
	private boolean ok;
	private int[][] board;
	private int num;

	private void core() throws Exception {
		int nrows = nextInt(), ncols = nextInt();
		hor = nextInt();
		ver = nextInt();
		square = nextInt();
		boolean swap = false;
		if ((nrows * ncols) % 2 == 1) {
			writer.println("IMPOSSIBLE");
		}
		else {
			if (nrows % 2 == 1) {
				swap = true;
				int t = nrows;
				nrows = ncols;
				ncols = t;
				t = hor;
				hor = ver;
				ver = t;
			}
			board = new int[nrows][ncols];
			for (int[] is: board) {
				Arrays.fill(is, -1);
			}
			ok = true;
			num = 0;
			if (ncols % 2 == 1) {
				for (int i = 0; i < nrows; i+=2) {
					putVer(i, ncols-1);
					putAll(i, 0, i+1, ncols-2);
				}
			}
			else {
				for (int i = 0; i < nrows; i+=2) {
					putAll(i, 0, i+1, ncols-1);
				}
			}
			if (!ok) {
				writer.println("IMPOSSIBLE");
			}
			else {
				if (swap) {
					int[][] temp = new int[ncols][nrows];
					for (int i = 0; i < temp.length; i++) {
						for (int j = 0; j < temp[0].length; j++) {
							temp[i][j] = board[j][i];
						}
					}
					board = temp;
				}
				LinkedList<Integer>[] adj = new LinkedList[num];
				for (int i = 0; i < adj.length; i++) {
					adj[i] = new LinkedList<Integer>();
				}
				for (int i = 0; i < board.length; i++) {
					for (int j = 0; j < board[i].length; j++) {
						for (int di = -1; di <= 1; di++) {
							for (int dj = -1; dj <= 1; dj++) {
								if (di == 0 ^ dj == 0) {
									int ni = i + di;
									int nj = j + dj;
									if (0 <= ni && ni < board.length && 
											0 <= nj && nj < board[0].length) {
										int l = board[i][j];
										int r = board[ni][nj];
										if (l != r) {
											adj[l].add(r);
											adj[r].add(l);
										}
									}
								}
							}
						}
					}
				}
				char[] id = new char[num];
				for (int i = 0; i < id.length; i++) {
					for (char ch = 'a';; ch++) {
						boolean ok = true;
						for (int j : adj[i]) {
							if (id[j] == ch) {
								ok = false;
								break;
							}
						}
						if (ok) {
							id[i] = ch;
							break;
						}
					}
				}
				for (int i = 0; i < board.length; i++) {
					for (int j = 0; j < board[0].length; j++) {
						writer.print(id[board[i][j]]);
					}
					writer.println();
				}
			}
		}
	}
	private void putAll(int i, int j, int i2, int j2) {
		for (int c = j; c <= j2; c+=2) {
			if (square > 0) {
				--square;
				board[i][c] = board[i+1][c] = board[i][c+1] = board[i+1][c+1] = num++; 
			}
			else if (hor >= 2) {
				hor-=2;
				board[i][c] = board[i][c+1] = num++;
				board[i+1][c] = board[i+1][c+1] = num++;
			}
			else if (ver >= 2) {
				ver-=2;
				board[i][c] = board[i+1][c] = num++;
				board[i][c+1] = board[i+1][c+1] = num++;
			}
			else {
				ok = false;
				return;
			}
		}
	}
	private void putVer(int i, int j) {
		if (ver == 0) {
			ok = false;
			return;
		}
		board[i][j] = board[i+1][j] = num++;
		--ver;
	}
	void debug(Object...os) {
		System.out.println(Arrays.deepToString(os));
	}
	//--------------------- IO stuffs ---------------------
    public static void main(String[] args) throws InterruptedException {
        Thread thread = new Thread(new C());
        thread.start();
        thread.join();
    }
	public void run() {
        try {
        	reader = _ReadFromFile ? new BufferedReader(new FileReader(IN_FILE)) : new BufferedReader(new InputStreamReader(System.in));
        	writer = _WriteToFile ? new PrintWriter(OUT_FILE) : new PrintWriter(new BufferedOutputStream(System.out));
            tokenizer = null;
            core();
            reader.close();
            writer.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }
    int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }
    long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }
    double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
    String nextToken() throws Exception {
        while (tokenizer == null || !tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }
}