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Printing patterns
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Algorithms, Breadth First Search, Graphs, Implementation, Matrix

Problem
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You are required to form a matrix of size \(r\times c\) where \(r\) is the number of rows and \(c\) is the number of columns. You are required to form the waves of numbers around the provided center, \((C_i,\ C_j)\) (0-based indexing).

Example:

  • Size of the matrix: \(r = 9\) and \(c = 9\)
  • Center coordinates: \(C_i = 4\) and \(C_j = 4\) (0 based indexing)
  • Pattern:

            4 4 4 4 4 4 4 4 4 
            4 3 3 3 3 3 3 3 4 
            4 3 2 2 2 2 2 3 4 
            4 3 2 1 1 1 2 3 4 
            4 3 2 1 0 1 2 3 4 
            4 3 2 1 1 1 2 3 4 
            4 3 2 2 2 2 2 3 4 
            4 3 3 3 3 3 3 3 4 
            4 4 4 4 4 4 4 4 4

You are given the values of \(r,\ c,\ C_i,\ C_j\) (the values of \(C_i\) and \(C_j\) is 0-based indexed). Your task is to print the provided pattern.

Input format

The first line contains four integers \(r\), \(c\), \(C_i\), and \(C_j\) denoting the number of rows, number of columns, \(x\) coordinate of center, and \(y\) coordinate of center.

Output format

Print the pattern for the provided input.

Constraints

\(1 \le r \le 1e3\\ 1 \le c \le 1e3\\ 0 \le C_i < r\\ 0 \le C_j < c\)

SAMPLE INPUT
10 10 5 5
SAMPLE OUTPUT
5 5 5 5 5 5 5 5 5 5 
5 4 4 4 4 4 4 4 4 4 
5 4 3 3 3 3 3 3 3 4 
5 4 3 2 2 2 2 2 3 4 
5 4 3 2 1 1 1 2 3 4 
5 4 3 2 1 0 1 2 3 4 
5 4 3 2 1 1 1 2 3 4 
5 4 3 2 2 2 2 2 3 4 
5 4 3 3 3 3 3 3 3 4 
5 4 4 4 4 4 4 4 4 4 
Explanation

Given input have shown output.

Time Limit: 2.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB

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