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.InputStreamReader;
import java.util.StringTokenizer;


public class Main {
    
    static int n,m,a,b,c;
    static int needed;
    static char res[][] = new char[110][110];
    static int dx[] = {0, 1, 0, -1};
    static int dy[] = {-1, 0, 1, 0};
    
    // we assume the place where we put the plank is emppty
    static void fillWithPlank(int mostleftbottom_n, int mostleftbottom_m, int type) {
        
        //System.out.println(mostleftbottom_n+" "+mostleftbottom_m+" "+type);
        
        int i,j,k;
        int momy = mostleftbottom_n;
        int momx = mostleftbottom_m;
        int newx, newy;
        
        boolean taken[] = new boolean[26];
        for (i=0;i<26;i++)
            taken[i] = false;
        
        if (type == 0) {
            // type a plank
            momy = mostleftbottom_n;
            momx = mostleftbottom_m;
            
            for (k=0;k<4;k++) {
                newx = momx+dx[k];
                newy = momy+dy[k];
                
                if (res[newy][newx] != '#') {
                    taken[res[newy][newx]-'a'] = true;
                }
                
            }
            
            momy = mostleftbottom_n;
            momx = mostleftbottom_m+1;
            
            for (k=0;k<4;k++) {
                newx = momx+dx[k];
                newy = momy+dy[k];
                
                if (res[newy][newx] != '#') {
                    taken[res[newy][newx]-'a'] = true;
                }
                
            }
            
            for (k=0;k<26;k++) {
                if (taken[k] == false) {
                    
                    momy = mostleftbottom_n;
                    momx = mostleftbottom_m;
                    
                    res[momy][momx] = (char)('a'+k);
                    
                    momy = mostleftbottom_n;
                    momx = mostleftbottom_m+1;
                    
                    res[momy][momx] = (char)('a'+k);
                    
                    
                    return;
                }
            }
            
        } else {
            if (type == 1) {
                // type b plank
                momy = mostleftbottom_n;
                momx = mostleftbottom_m;
                
                for (k=0;k<4;k++) {
                    newx = momx+dx[k];
                    newy = momy+dy[k];
                    
                    if (res[newy][newx] != '#') {
                        taken[res[newy][newx]-'a'] = true;
                    }
                    
                }
                
                momy = mostleftbottom_n-1;
                momx = mostleftbottom_m;
                
                for (k=0;k<4;k++) {
                    newx = momx+dx[k];
                    newy = momy+dy[k];
                    
                    if (res[newy][newx] != '#') {
                        taken[res[newy][newx]-'a'] = true;
                    }
                    
                }
                
                for (k=0;k<26;k++) {
                    if (taken[k] == false) {
                        
                        momy = mostleftbottom_n;
                        momx = mostleftbottom_m;
                        
                        res[momy][momx] = (char)('a'+k);
                        
                        momy = mostleftbottom_n-1;
                        momx = mostleftbottom_m;
                        
                        res[momy][momx] = (char)('a'+k);
                        
                        
                        return;
                    }
                }
                
            } else {
                // type c plank
                momy = mostleftbottom_n;
                momx = mostleftbottom_m;
                
                
                for (k=0;k<4;k++) {
                    newx = momx+dx[k];
                    newy = momy+dy[k];
                    
                    if (res[newy][newx] != '#') {
                        taken[res[newy][newx]-'a'] = true;
                    }
                    
                }
                
                momy = mostleftbottom_n;
                momx = mostleftbottom_m+1;
                
                for (k=0;k<4;k++) {
                    newx = momx+dx[k];
                    newy = momy+dy[k];
                    
                    if (res[newy][newx] != '#') {
                        taken[res[newy][newx]-'a'] = true;
                    }
                    
                }
                
                momy = mostleftbottom_n-1;
                momx = mostleftbottom_m;
                
                for (k=0;k<4;k++) {
                    newx = momx+dx[k];
                    newy = momy+dy[k];
                    
                    if (res[newy][newx] != '#') {
                        taken[res[newy][newx]-'a'] = true;
                    }
                    
                }
                
                momy = mostleftbottom_n-1;
                momx = mostleftbottom_m+1;
                
                for (k=0;k<4;k++) {
                    newx = momx+dx[k];
                    newy = momy+dy[k];
                    
                    if (res[newy][newx] != '#') {
                        taken[res[newy][newx]-'a'] = true;
                    }
                    
                }
                
                for (k=0;k<26;k++) {
                    if (taken[k] == false) {
                        
                        
                        momy = mostleftbottom_n;
                        momx = mostleftbottom_m;
                        
                        res[momy][momx] = (char)('a'+k);
                        
                        momy = mostleftbottom_n;
                        momx = mostleftbottom_m+1;
                        
                        res[momy][momx] = (char)('a'+k);
                        
                        momy = mostleftbottom_n-1;
                        momx = mostleftbottom_m;
                        
                        res[momy][momx] = (char)('a'+k);
                        
                        momy = mostleftbottom_n-1;
                        momx = mostleftbottom_m+1;
                        
                        res[momy][momx] = (char)('a'+k);
                        
                        return;
                    }
                }
            }
        }
    }
    
    static void printMatrix() {
        int i,j;
        
        for (i=1;i<=n;i++) {
            for (j=1;j<=m;j++) {
                System.out.print(res[i][j]);
            }
            System.out.println();
        }
        
    }
    
    public static void main(String[] args) throws Exception {
        int i,j,k;
        int pm,pn;
        
        for (i=0;i<110;i++) {
            for (j=0;j<110;j++) {
                res[i][j] = '#';
            }
        }
        
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.readLine());
        
        n = Integer.parseInt(st.nextToken());
        m = Integer.parseInt(st.nextToken());
        a = Integer.parseInt(st.nextToken());
        b = Integer.parseInt(st.nextToken());
        c = Integer.parseInt(st.nextToken());
        
        
        if ((n*m)%2==1) {
            System.out.println("IMPOSSIBLE");
            return;
        }
        
        // at least one dimension is even number
        
        if ((n%2 == 0)&&(m%2 == 0)) {
            // we want to make blocks 2x2
            pn = n;
            pm = m;
        } else {
            // one dimension is odd number
            
            if (n%2 == 1) {
                // we need a blocks
                
                needed = m/2;
                if (needed > a) {
                    System.out.println("IMPOSSIBLE");
                    return;
                } else {
                    // we give needed number of blocks for filling the lowest row
                    a -= needed;
                    
                    j = 1;
                    for (i=0;i<needed;i++) {
                        fillWithPlank(n, j, 0);
                        j += 2;
                    }
                    
                }
                
                pm = m;
                pn = n-1;
                
            } else {
                // we need b blocks
                
                needed = n/2;
                if (needed > b) {
                    System.out.println("IMPOSSIBLE");
                    return;
                } else {
                    // we give needed number of blocks for filling the most right column
                    b -= needed;
                    
                    j = 2;
                    for (i=0;i<needed;i++) {
                        fillWithPlank(j, m, 1);
                        j += 2;
                    }
                    
                }
                
                pm = m-1;
                pn = n;
                
            }
        }
        
        
        // checking
        needed = (pm*pn)/4;
        
        
        int total = 0;
        
        // we are trying to make blocks 2x2
        total += c;
        total += (a/2);
        total += (b/2);
        
        if (total < needed) {
            System.out.println("IMPOSSIBLE");
            return;
        }
        
        
        // if the checking is good
        
        for (i=2;i<=pn;i+=2) {
            for (j=1;j<=pm;j+=2) {
                
                //System.out.println(i+" "+j+" :");
                
                if (c > 0) {
                    c--;
                    
                    //System.out.println("C: "+c);
                    
                    fillWithPlank(i, j, 2);
                    
                } else {
                    if (a >= 2) {
                        a -= 2;
                        fillWithPlank(i-1, j, 0);
                        fillWithPlank(i, j, 0);
                    } else {
                        b -= 2;
                        fillWithPlank(i, j, 1);
                        fillWithPlank(i, j+1, 1);
                    }
                }
                
            }
        }
        
        printMatrix();
        
    }

}