Kessoku Band Poster

Ryo and Kita want to design a poster for Kessoku Band. The poster is a 2-D grid with N rows and M columns containing lowercase English letters. They want the grid to satisfy their peculiar palindrome tastes. Ryo requires that exactly R rows are palindromic while Kita requires that exactly C columns are palindromic.

A string (or a row/column of letters) is a palindrome if it reads the same forwards and backwards. For example, kayak and bb are palindromes.

Your task is to either construct such a grid or determine that it is impossible. In case a solution exists, output the grid; otherwise, output -1.

Note. If a row (or column) does not satisfy the palindrome property it is considered non‐palindromic.

The constraints guarantee that if a solution exists then
\( N \ge 2,\; M \ge 2 \), and in any valid input if either R<N or C<M then it is required that there is at least one row (or column) available for modification. In our intended solution we assume R > 0 (so at least one row is mandated to be palindromic) and C < M (so that at least one column is non‐palindromic) in the cases where modifications are needed. (Otherwise, when R = N and C = M the unique solution is the grid with all cells equal to 'a'.)

The following constructive approach is used (when a solution is possible):

1. Initialize the grid with all letters 'a' (so every row and column is a palindrome).
2. If exactly R rows must be palindromic then N − R rows must be made non‐palindromic. Let the set of these rows be B. To break the horizontal palindrome property in a row, it suffices to change one letter in a position such that it does not equal its mirror. However, to avoid undesirable effects on columns that are required to be palindromic, we force any horizontal change to occur in a column that is allowed to be non–palindromic.
3. Similarly, exactly M − C columns must be non–palindromic. A column is broken if at least one vertical pair (i, N−1−i) has differing letters.
4. In our simple construction we choose the first M − C columns as the set Q allowed to be non–palindromic. Then, for the first break row in B we change every cell in these chosen columns to 'b' (thus this row becomes non–palindromic because the mirror cells remain 'a'). For every other break row we change just one cell (the first column in Q) to 'b'. This guarantees that every row in B is non–palindromic and every column in Q gets at least one vertical mismatch (when compared with a row that is not broken in that column). Meanwhile, the rows not in B remain all 'a' (horizontally palindromic) and every column outside Q remains unaffected (thus palindromic).

If any of the simple feasibility conditions is not met – for example when M = 1 (thus every column is automatically a palindrome) but C ≠ 1, or when R = 0 – then the answer is -1.

inputFormat

The input consists of four space‐separated integers: N, M, R and C.

Constraints (assumed for this problem):

• \( N, M \ge 2 \) when modifications are needed; if \(N = 1\) or \(M = 1\) the only valid case is when \(R = 1\) and \(C = 1\).
• If \(R < N\) then at least one row is available to be broken.
• If \(C < M\) then at least one column is available to be broken.

outputFormat

If a valid grid exists, output N lines. Each line should contain a string of M lowercase letters representing the corresponding row of the poster. If no valid grid exists, output a single line with -1.

sample

4 5 2 3

bbaaa
baaaa
aaaaa
aaaaa