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.math.BigDecimal;
import java.math.BigInteger;
import java.math.RoundingMode;
import java.util.*;

/**
 * @author Tran Anh Tai
 * @template for CP codes
 * What a trick prob!
 */
public class ProbA {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(in, out);
        out.close();
    }
    // main solver
    static class Task{
        static int MOD = 1000000007;
        public void solve(InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();
            if (m % 2 == 1 && n % 2 == 1){
                out.println("IMPOSSIBLE");
            }
            else if (m * n > a * 2 + b * 2 + c * 4){
                out.println("IMPOSSIBLE");
            }
            else{
                char[][] board = new char[n][m];
                int type1 = 0;
                int type2 = 0;
                int row = 0;
                int coll = 0;
                if (m % 2 == 0 && n % 2 == 0){ // then both type 1 and type 2 planks should be even;
                    if ((m * n == a * 2 + b * 2 + c * 4) && a % 2 == 1){
                        out.println("IMPOSSIBLE");
                        return;
                    }
                    else{
                        if (4 * c < m * n){
                            type1 = a - a % 2;
                            type2 = (m * n - 2 * type1 - 4 * c) / 2;
                            if (type2 < 0){
                                type2 = 0;
                                type1 = (m * n - 4 * c) / 2;
                            }
                        }
                    }
                }
                else if (m % 2 == 0){// then the number of type 2 should be even; -> required some type1 amount;
                    if (a < m / 2){
                        out.println("IMPOSSIBLE"); return;
                    }
                    a -= m / 2;
                    row = 1;
                    for (int i = 0; i < m; i += 2){
                        board[0][i] = board[0][i + 1] = (char)('a' + i % 26);
                    }
                    if (m * n - m < 4 * c){
                        type1 = 0; type2 = 0;
                    }
                    else if (m * n - m < 4 * c + b * 2){
                        type1 = 0;
                        type2 = (m * n- m - 4 * c) / 2;
                    }
                    else{
                        type2 = b;
                        type1 = (m * n - m - 4 * c - type2 * 2) / 2;
                    }
                }
                else{
                    if (b < n / 2){
                        out.println("IMPOSSIBLE"); return;
                    }
                    b -= n / 2;
                    coll = 1;
                    for (int i = 0; i < n; i += 2){
                        board[i][0] = board[i + 1][0] = (char)('a' + i % 26);
                    }
                    if (m * n - n < 4 * c){
                        type1 = 0; type2 = 0;
                    }
                    else if (m * n - n < 4 * c + 2 * a){
                        type1 = (m * n - 4 * c) / 2; type2  = 0;
                    }
                    else{
                        type1 = a;
                        type2 = (m * n - 4 * c - 2 * a) / 2;
                    }
                }
                while (row < n){
                    int col = coll; // reset;
                    while (col < m){
                        List<Character>  exclude = new ArrayList<>();
                        if (row > 0){
                            exclude.add(board[row - 1][col]);
                            exclude.add(board[row - 1][col + 1]);
                        }
                        if (col > 0){
                            exclude.add(board[row][col - 1]);
                            exclude.add(board[row + 1][col - 1]);
                        }
                        char[] fill = getMex(exclude);
                        if (c > 0){
                            board[row][col] = fill[0];
                            board[row + 1][col] = fill[0];
                            board[row][col +1] = fill[0];
                            board[row + 1][col + 1] = fill[0];
                            c--;
                        }
                        else if (type1 > 0){
                            board[row][col] = fill[0];
                            board[row + 1][col] = fill[1];
                            board[row][col +1] = fill[0];
                            board[row + 1][col + 1] = fill[1];
                            type1 -= 2;
                        }
                        else if (type2 > 0){
                            board[row][col] = fill[0];
                            board[row + 1][col] = fill[0];
                            board[row][col +1] = fill[1];
                            board[row + 1][col + 1] = fill[1];
                            type2 -= 2;
                        }
                        col += 2;
                    }
                    row += 2;
                }
                for (row = 0; row < n; row++){
                    for (int col = 0; col < m; col++){
                        out.print(board[row][col]);
                    }
                    out.println();
                }
            }
        }

        private char[] getMex(List<Character> exclude) {
            char[] result = new char[2];
            result[0] = ' ';
            result[1] = ' ';
            for (char ch = 'a'; ch <= 'z'; ch++){
                if (!exclude.contains(ch)){
                    if (result[0] == ' '){
                        result[0] = ch;
                    }
                    else if (result[1] == ' '){
                        result[1] = ch;
                        return result;
                    }
                }
            }
            return result;
        }
    }
    // fast input reader class;
    static class InputReader {
        BufferedReader br;
        StringTokenizer st;

        public InputReader(InputStream stream) {
            br = new BufferedReader(new InputStreamReader(stream));
        }

        public String nextToken() {
            while (st == null || !st.hasMoreTokens()) {
                String line = null;
                try {
                    line = br.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (line == null) {
                    return null;
                }
                st = new StringTokenizer(line);
            }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(nextToken());
        }
        public long nextLong(){
            return Long.parseLong(nextToken());
        }
    }
}