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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 *         Created on 14.03.2010
 */
public class TaskC implements Runnable {
	private InputReader in;
	private PrintWriter out;

	public static void main(String[] args) {
		new Thread(new TaskC()).start();
//		new Template().run();
	}

	public TaskC() {
//		String id = getClass().getName().toLowerCase();
//		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
//		} catch (FileNotFoundException e) {
//			throw new RuntimeException();
//		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	public void run() {
//        int numTests = in.readInt();
//        for (int testNumber = 0; testNumber < numTests; testNumber++) {
//			out.print("Case " + (testNumber + 1) + ": ");
//        }
		int n = in.readInt();
		int m = in.readInt();
		int a = in.readInt();
		int b = in.readInt();
		int c = in.readInt();
		char[][] t = new char[n][m];
		if (n % 2 == 1) {
			if (m % 2 == 1) {
				out.println("IMPOSSIBLE");
				out.close();
				return;
			}
			if (a >= m / 2) {
				a -= m / 2;
				for (int j = 0; j < m / 2; j++) {
					char cur = 'y';
					if (j % 2 == 1)
						cur = 'z';
					t[n - 1][2 * j] = t[n - 1][2 * j + 1] = cur;
				}
				n--;
			} else {
				out.println("IMPOSSIBLE");
				out.close();
				return;
			}
		}
		if (m % 2 == 1) {
			if (b >= n / 2) {
				b -= n / 2;
				for (int j = 0; j < n / 2; j++) {
					char cur = 'y';
					if (j % 2 == 1)
						cur = 'z';
					t[2 * j][m - 1] = t[2 * j + 1][m - 1] = cur;
				}
				m--;
			} else {
				out.println("IMPOSSIBLE");
				out.close();
				return;
			}
		}
		if (c + a / 2 + b / 2 < m * n / 4) {
			out.println("IMPOSSIBLE");
			out.close();
			return;
		}
		for (int i = 0; i < n / 2; i++) {
			for (int j = 0; j < m / 2; j++) {
				char cur = (char) ('a' + ((i % 2) * 2 + (j % 2)) * 2);
				if (c != 0) {
					t[2 * i][2 * j] = t[2 * i + 1][2 * j] = t[2 * i][2 * j + 1] = t[2 * i + 1][2 * j + 1] = cur;
					c--;
				} else if (a >= 2) {
					a -= 2;
					t[2 * i][2 * j] = t[2 * i][2 * j + 1] = cur;
					t[2 * i + 1][2 * j] = t[2 * i + 1][2 * j + 1] = (char) (cur + 1);
				} else {
					t[2 * i][2 * j] = t[2 * i + 1][2 * j] = cur;
					t[2 * i][2 * j + 1] = t[2 * i + 1][2 * j + 1] = (char) (cur + 1);					
				}
			}
		}
		for (char[] aT : t) {
			for (char anAT : aT)
				out.print(anAT);
			out.println();
		}
		out.close();
	}

	private static class InputReader {
		private InputStream stream;
		private byte[] buf = new byte[1000];
		private int curChar, numChars;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		private int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		public String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		private boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		public String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		public String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		public BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		public char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		public double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}