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.util.*;
import java.io.*;
import java.math.BigInteger;

public class Main implements Runnable {
	static final String no = "IMPOSSIBLE";

	private void solution() throws IOException {
		int n = in.nextInt();
		int m = in.nextInt();
		int a12 = in.nextInt();
		int a21 = in.nextInt();
		int a22 = in.nextInt();
		if (n * m % 2 == 1) {
			out.println(no);
			return;
		}
		char[][] grid = new char[n][m];
		if (n % 2 == 1) {
			int need = m / 2;
			if (a12 < need) {
				out.println(no);
				return;
			} else {
				char c = 'x';
				for (int i = 0; i < m; i += 2) {
					grid[n - 1][i] = c;
					grid[n - 1][i + 1] = c;
					c ^= 1;
				}
				a12 -= need;
				--n;
			}
		} else if (m % 2 == 1) {
			int need = n / 2;
			if (a21 < need) {
				out.println(no);
				return;
			} else {
				char c = 'x';
				for (int i = 0; i < n; i += 2) {
					grid[i][m - 1] = c;
					grid[i + 1][m - 1] = c;
					c ^= 1;
				}
				a21 -= need;
				--m;
			}
		}
		int t12 = a12 / 2;
		int t21 = a21 / 2;
		int t22 = a22;
		if (4 * (t12 + t21 + t22) < n * m) {
			out.println(no);
		} else {
			char c = 'a';
			for (int i = 0; i < n; i += 2) {
				for (int j = 0; j < m; j += 2) {
					if (t12 > 0) {
						grid[i][j] = c;
						grid[i][j + 1] = c;
						grid[i + 1][j] = (char) (c + 1);
						grid[i + 1][j + 1] = (char) (c + 1);
						--t12;
					} else if (t21 > 0) {
						grid[i][j] = (char) (c + 2);
						grid[i + 1][j] = (char) (c + 2);
						grid[i][j + 1] = (char) (c + 3);
						grid[i + 1][j + 1] = (char) (c + 3);
						--t21;
					} else {
						for (int dx = 0; dx < 2; ++dx) {
							for (int dy = 0; dy < 2; ++dy) {
								grid[i + dx][j + dy] = (char) (c + 4);
							}
						}
					}
					if (j / 2 % 2 == 0) {
						c += 5;
					} else {
						c -= 5;
					}
				}
				if (i / 2 % 2 == 0) {
					c = 'a' + 10;
				} else {
					c = 'a';
				}
			}
			for (char[] t : grid) {
				out.println(new String(t));
			}
		}
	}

	public void run() {
		try {
			// in = new Scanner(new FileReader(fileName + ".in"));
			// out = new PrintWriter(fileName + ".out");
			solution();
			in.reader.close();
			out.close();
		} catch (Exception e) {
			e.printStackTrace();
			System.exit(1);
		}
	}
	String fileName = "";

	private class Scanner {
		BufferedReader reader;
		StringTokenizer tokenizer;

		public Scanner(Reader reader) {
			this.reader = new BufferedReader(reader);
			this.tokenizer = new StringTokenizer("");
		}

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

		public boolean hasNext() throws IOException {
			while (!tokenizer.hasMoreTokens()) {
				String next = reader.readLine();
				if (next == null) {
					return false;
				}
				tokenizer = new StringTokenizer(next);
			}
			return true;
		}

		public String next() throws IOException {
			hasNext();
			return tokenizer.nextToken();
		}

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

		public String nextLine() throws IOException {
			tokenizer = new StringTokenizer("");
			return reader.readLine();
		}
	}

	public static void main(String[] args) throws IOException {
		new Thread(null, new Main(), "", 1 << 28).start();
	}
	PrintWriter out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
	Scanner in = new Scanner(new InputStreamReader(System.in));
}