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 static java.util.Arrays.*;
import static java.lang.Math.*;
import static java.math.BigInteger.*;
import java.util.*;
import java.math.*;
import java.io.*;

public class C implements Runnable
{
    String file = "input";
    
    void init() throws IOException
    {
        //input = new BufferedReader(new FileReader(file + ".in"));
        input = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(new BufferedOutputStream(System.out));
    }
    
    void solve() throws IOException
    {
        int rn = nextInt(), cn = nextInt(), a = nextInt(), b = nextInt(), c = nextInt();
        this.rn = rn; this.cn = cn;
        cs = new char[rn][cn];
        if(solve(a, b, c, rn, cn)) for(int i = 0; i < cs.length; i++) out.println(cs[i]);
        else out.println("IMPOSSIBLE"); 
    }
    char[][] cs;
    
    boolean solve(int a, int b, int c, int rn, int cn)
    {
        if(rn % 2 == 1)
        {
            if(cn % 2 == 1) return false;
            for(int j = 0; j < cn; j += 2)
            {
                put(rn - 1, rn - 1, j, j + 1);
                if(--a < 0) return false;
            }
            rn--;
        }
        else if(cn % 2 == 1)
        {
            for(int i = 0; i < rn; i += 2)
            {
                put(i, i + 1, cn - 1, cn - 1);
                if(--b < 0) return false;
            }
            cn--;
        }
        for(int i = 0; i < rn; i += 2)
            for(int j = 0; j < cn; j += 2)
                if(c > 0) 
                {
                    put(i, i + 1, j, j + 1);
                    c--;
                }
                else if(a > 1)
                {
                    put(i, i, j, j + 1);
                    put(i + 1, i + 1, j, j + 1);
                    a--; a--;
                }
                else if(b > 1)
                {
                    put(i, i + 1, j, j);
                    put(i, i + 1, j + 1, j + 1);
                    b--; b--;
                }
                else return false;
        return true;
    }
    int rn, cn;
    void put(int x1, int x2, int y1, int y2)
    {
        boolean[] had = new boolean[300];
        if(x1 > 0) for(int y = y1; y <= y2; y++) had[cs[x1 - 1][y]] = true;
        if(x2 + 1 < rn) for(int y = y1; y <= y2; y++) had[cs[x2 + 1][y]] = true;
        if(y1 > 0) for(int x = x1; x <= x2; x++) had[cs[x][y1 - 1]] = true;
        if(y2 + 1 < cn) for(int x = x1; x <= x2; x++) had[cs[x][y2 + 1]] = true;
        for(int i = 0; i < 26; i++)
            if(!had[i + 'a'])
            {
                for(int x = x1; x <= x2; x++)
                    for(int y = y1; y <= y2; y++)
                        cs[x][y] = (char)(i + 'a');
                return;
            }
    }
    
    String next() throws IOException
    {
        while(st == null || !st.hasMoreTokens()) st = new StringTokenizer(input.readLine());
        return st.nextToken();
    }
    
    int nextInt() throws IOException
    {
        return Integer.parseInt(next());
    }
    
    long nextLong() throws IOException
    {
        return Long.parseLong(next());
    }
    
    double nextDouble() throws IOException
    {
        return Double.parseDouble(next());
    }
    
    void print(Object... o)
    {
        System.out.println(deepToString(o));
    }
    
    void gcj(Object o)
    {
        String s = String.valueOf(o);
        out.println("Case #" + test + ": " + s);
        System.out.println("Case #" + test + ": " + s);
    }
    
    BufferedReader input;
    PrintWriter out;
    StringTokenizer st;
    int test;
    
    public static void main(String[] args) throws IOException
    {
        new Thread(null, new C(), "", 1 << 20).start();
    }
    
    public void run()
    {
        try
        {
            init();
            solve();
            out.close();        
        }
        catch(Exception e)
        {
            e.printStackTrace();
            System.exit(1);
        }
    }
}