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.BufferedReader;
import java.io.FileInputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.Iterator;
import java.util.StringTokenizer;

public class Main {

    public static void main(String[] args) throws Exception {
        //System.setIn(new FileInputStream("1"));
        in = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);

        solve();

        in.close();
        out.close();
    }

    private static void solve() throws Exception {
        int n = nextInt(), m = nextInt(), a = nextInt(), b = nextInt(), c = nextInt();
        if (n % 2 != 0 && m % 2 != 0) {
            out.println("IMPOSSIBLE");
            return;
        }
        char[][] field = new char[n][m];
        if (n % 2 == 0 && m % 2 == 0) {
            if (!put(field, n, m, a, b, c))
                out.println("IMPOSSIBLE");
            else
                out(field);
            return;
        }
        if (n % 2 != 0) {
            if (!put(field, n - 1, m, a - m / 2, b, c))
                out.println("IMPOSSIBLE");
            else {
                HashSet<Character> set = new HashSet<Character>();
                for (char v = 'a'; v <= 'z'; v++)
                    set.add(v);
                
                int i = n - 1;
                for (int j = 0; j < m; j += 2) {
                    if (i > 0) {
                        set.remove(field[i - 1][j]);
                        set.remove(field[i - 1][j + 1]);
                    }
                    if (j > 0) {
                        set.remove(field[i][j - 1]);
                    }

                    char v = set.iterator().next();
                    field[i][j] = field[i][j + 1] = v;
                    
                    if (i > 0) {
                        set.add(field[i - 1][j]);
                        set.add(field[i - 1][j + 1]);
                    }
                    if (j > 0) {
                        set.add(field[i][j - 1]);
                    }

                }
                out(field);
            }
            return;
        }
        if (!put(field, n, m - 1, a, b - n / 2, c))
            out.println("IMPOSSIBLE");
        else {
            HashSet<Character> set = new HashSet<Character>();
            for (char v = 'a'; v <= 'z'; v++)
                set.add(v);

            int j = m - 1;
            for (int i = 0; i < n; i += 2) {
                
                if (i > 0) {
                    set.remove(field[i - 1][j]);
                }
                if (j > 0) {
                    set.remove(field[i][j - 1]);
                    set.remove(field[i + 1][j - 1]);
                }

                char v = set.iterator().next();
                field[i][j] = field[i + 1][j] = v;
                
                if (i > 0) {
                    set.add(field[i - 1][j]);
                }
                if (j > 0) {
                    set.add(field[i][j - 1]);
                    set.add(field[i + 1][j - 1]);
                }
            }
            out(field);
        }
    }

    private static boolean put(char[][] field, int n, int m, int a, int b, int c) {
        if (a < 0)
            return false;
        if (b < 0)
            return false;
        
        a /= 2;
        b /= 2;
        
        if (n * m / 4 > a + b + c)
            return false;
        
        if (n == 0)
            return true;
        if (m == 0)
            return true;
        
        HashSet<Character> set = new HashSet<Character>();
        for (char v = 'a'; v <= 'z'; v++)
            set.add(v);
        
        int i = 0, j = 0;
        
        loop1: for (; i < n; i += 2) {
            for (; j < m; j += 2) {
                if (c == 0)
                    break loop1;
                
                if (i > 0) {
                    set.remove(field[i - 1][j]);
                    set.remove(field[i - 1][j + 1]);
                }
                if (j > 0) {
                    set.remove(field[i][j - 1]);
                    set.remove(field[i + 1][j - 1]);
                }
                
                char v = set.iterator().next();
                field[i][j] = field[i + 1][j] = field[i][j + 1] = field[i + 1][j + 1] = v;
                --c;
                
                if (i > 0) {
                    set.add(field[i - 1][j]);
                    set.add(field[i - 1][j + 1]);
                }
                if (j > 0) {
                    set.add(field[i][j - 1]);
                    set.add(field[i + 1][j - 1]);
                }

            }
            j = 0;
        }
        
        loop2: for (; i < n; i += 2) {
            for (; j < m; j += 2) {
                if (a == 0)
                    break loop2;
                
                if (i > 0) {
                    set.remove(field[i - 1][j]);
                    set.remove(field[i - 1][j + 1]);
                }
                if (j > 0) {
                    set.remove(field[i][j - 1]);
                    set.remove(field[i + 1][j - 1]);
                }
                
                Iterator<Character> it = set.iterator();
                char v1 = it.next();
                char v2 = it.next();
                
                field[i][j] = field[i][j + 1] = v1;
                field[i + 1][j] = field[i + 1][j + 1] = v2;
                --a;
                
                if (i > 0) {
                    set.add(field[i - 1][j]);
                    set.add(field[i - 1][j + 1]);
                }
                if (j > 0) {
                    set.add(field[i][j - 1]);
                    set.add(field[i + 1][j - 1]);
                }

            }
            j = 0;
        }

        loop3: for (; i < n; i += 2) {
            for (; j < m; j += 2) {
                if (b == 0)
                    break loop3;
                
                if (i > 0) {
                    set.remove(field[i - 1][j]);
                    set.remove(field[i - 1][j + 1]);
                }
                if (j > 0) {
                    set.remove(field[i][j - 1]);
                    set.remove(field[i + 1][j - 1]);
                }
                
                Iterator<Character> it = set.iterator();
                char v1 = it.next();
                char v2 = it.next();
                
                field[i][j] = field[i + 1][j] = v1;
                field[i][j + 1] = field[i + 1][j + 1] = v2;
                --b;
                
                if (i > 0) {
                    set.add(field[i - 1][j]);
                    set.add(field[i - 1][j + 1]);
                }
                if (j > 0) {
                    set.add(field[i][j - 1]);
                    set.add(field[i + 1][j - 1]);
                }
            }
            j = 0;
        }

        return true;
    }

    private static void out(char[][] field) {
        for (int i = 0; i < field.length; i++) {
            out.println(new String(field[i]));
        }
    }

    static BufferedReader in;
    static PrintWriter out;
    static StringTokenizer st;

    static String nextString() throws IOException {
        while (st == null || !st.hasMoreTokens()) {
            st = new StringTokenizer(in.readLine());
        }
        return st.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(nextString());
    }

    static double nextDouble() throws IOException {
        return Double.parseDouble(nextString());
    }
}