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.*;
import java.util.*;
import java.math.*;

public class C implements Runnable {
	static BufferedReader in;
	static PrintWriter out;
	static StringTokenizer st;
	static Random rnd;

	private void solve() throws IOException {
		int n = nextInt(), m = nextInt(), a = nextInt(), b = nextInt(), c = nextInt();
		int s = n * m;

		if (s % 2 != 0) {
			fail();
		} else if (n % 2 == 0 && m % 2 == 0) {
			int[][] result = new int[n][m];
			int id = 0;
			for (int i = 0; i < n; i += 2) {
				for (int j = 0; j < m; j += 2) {
					if (c >= 1) {
						result[i][j] = id;
						result[i + 1][j] = id;
						result[i][j + 1] = id;
						result[i + 1][j + 1] = id;
						++id;
						--c;
					} else if (a >= 2) {
						result[i][j] = id;
						result[i][j + 1] = id;
						++id;
						--a;
						result[i + 1][j] = id;
						result[i + 1][j + 1] = id;
						++id;
						--a;
					} else if (b >= 2) {
						result[i][j] = id;
						result[i + 1][j] = id;
						++id;
						--b;
						result[i][j + 1] = id;
						result[i + 1][j + 1] = id;
						++id;
						--b;
					} else {
						fail();
					}
				}
			}
			printAnswer(n, m, result);
		} else if (m % 2 != 0) {
			int[][] result = new int[n][m];
			int id = 0;
			for (int i = 0; i < n; i += 2) {
				for (int j = 0; j < m - 1; j += 2) {
					if (c >= 1) {
						result[i][j] = id;
						result[i + 1][j] = id;
						result[i][j + 1] = id;
						result[i + 1][j + 1] = id;
						++id;
						--c;
					} else if (a >= 2) {
						result[i][j] = id;
						result[i][j + 1] = id;
						++id;
						--a;
						result[i + 1][j] = id;
						result[i + 1][j + 1] = id;
						++id;
						--a;
					} else if (b >= 2) {
						result[i][j] = id;
						result[i + 1][j] = id;
						++id;
						--b;
						result[i][j + 1] = id;
						result[i + 1][j + 1] = id;
						++id;
						--b;
					} else {
						fail();
					}
				}
			}
			for (int i = 0; i < n; i += 2) {
				if (b >= 1) {
					result[i][m - 1] = id;
					result[i + 1][m - 1] = id;
					++id;
					--b;
				} else {
					fail();
				}
			}
			printAnswer(n, m, result);
		} else if (n % 2 != 0) {
			int[][] result = new int[n][m];
			int id = 0;
			for (int i = 0; i < n - 1; i += 2) {
				for (int j = 0; j < m; j += 2) {
					if (c >= 1) {
						result[i][j] = id;
						result[i + 1][j] = id;
						result[i][j + 1] = id;
						result[i + 1][j + 1] = id;
						++id;
						--c;
					} else if (b >= 2) {
						result[i][j] = id;
						result[i + 1][j] = id;
						++id;
						--b;
						result[i][j + 1] = id;
						result[i + 1][j + 1] = id;
						++id;
						--b;
					} else if (a >= 2) {
						result[i][j] = id;
						result[i][j + 1] = id;
						++id;
						--a;
						result[i + 1][j] = id;
						result[i + 1][j + 1] = id;
						++id;
						--a;
					} else {
						fail();
					}
				}
			}
			for (int i = 0; i < m; i += 2) {
				if (a >= 1) {
					result[n - 1][i] = id;
					result[n - 1][i + 1] = id;
					++id;
					--a;
				} else {
					fail();
				}
			}
			printAnswer(n, m, result);
		} else {
			throw new AssertionError();
		}
	}

	private void fail() {
		out.println("IMPOSSIBLE");
		out.flush();
		out.close();
		System.exit(0);
	}

	private void printAnswer(int n, int m, int[][] result) {
		int maxId = 0;
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				maxId = Math.max(maxId, result[i][j]);
			}
		}
		boolean[] already = new boolean[maxId + 1];
		char[] idToChar = new char[maxId + 1];
		boolean[] cant = new boolean[26];
		int[] dx = { 1, -1, 0, 0 };
		int[] dy = { 0, 0, 1, -1 };
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				int id = result[i][j];
				if (!already[id]) {
					Arrays.fill(cant, false);
					for (int si = 0; si <= 1; si++) {
						for (int sj = 0; sj <= 1; sj++) {
							int ni = i + si, nj = j + sj;
							if (ni < n && nj < m && result[ni][nj] == id) {
								for (int k = 0; k < 4; k++) {
									int bi = ni + dx[k], bj = nj + dy[k];
									if (bi >= 0 && bj >= 0 && bi < n && bj < m) {
										int bid = result[bi][bj];
										if (id != bid && already[bid]) {
											cant[idToChar[bid] - 'a'] = true;
										}
									}
								}
							}
						}
					}
					int c = 0;
					while (cant[c])
						++c;
					if (c >= 4)
						throw new AssertionError();
					already[id] = true;
					idToChar[id] = (char) ('a' + c);
				}
			}
		}
		for (int i = 0; i < n; i++) {
			for (int j = 0; j < m; j++) {
				if (!already[result[i][j]])
					throw new AssertionError();
				out.print(idToChar[result[i][j]]);
			}
			out.print('\n');
		}
	}

	public static void main(String[] args) {
		// final boolean oldChecker = false;
		//
		// if (oldChecker)
		// new Thread(null, new Template(), "yarrr", 1 << 24).start();
		// else
		new C().run();
	}

	public void run() {
		try {
			final String className = this.getClass().getName().toLowerCase();

			try {
				in = new BufferedReader(new FileReader(className + ".in"));
				out = new PrintWriter(new FileWriter(className + ".out"));
				// in = new BufferedReader(new FileReader("input.txt"));
				// out = new PrintWriter(new FileWriter("output.txt"));
			} catch (FileNotFoundException e) {
				in = new BufferedReader(new InputStreamReader(System.in));
				out = new PrintWriter(System.out);
			}

			rnd = new Random();

			solve();

			out.close();
		} catch (IOException e) {
			e.printStackTrace();
			System.exit(1);
		}
	}

	private String nextToken() throws IOException {
		while (st == null || !st.hasMoreTokens()) {
			String line = in.readLine();

			if (line == null)
				return null;

			st = new StringTokenizer(line);
		}

		return st.nextToken();
	}

	private int nextInt() throws IOException {
		return Integer.parseInt(nextToken());
	}

	private long nextLong() throws IOException {
		return Long.parseLong(nextToken());
	}

	private double nextDouble() throws IOException {
		return Double.parseDouble(nextToken());
	}
}