You have been given a matrix of ‘N’ rows and ‘M’ columns filled up with integers. Find the minimum sum that can be obtained from a path which from cell (x,y) and ends at the top left corner (1,1).
From any cell in a row, we can move to the right, down or the down right diagonal cell. So from a particular cell (row, col), we can move to the following three cells:
Down: (row+1,col)
Right: (row, col+1)
Down right diagonal: (row+1, col+1)
The first line will contain two integers ‘N’ and ‘M’ denoting the number of rows and columns, respectively.
Next ‘N’ lines contain ‘M’ space-separated integers each denoting the elements in the matrix.
The last line will contain two integers ‘x’ and ‘y’ denoting the cell to start from.
For each test case, print an integer that represents the minimum sum that can be obtained by traveling a path as described above.
Output for every test case will be printed in a separate line.
Note:
You don’t need to print anything; It has already been taken care of.
Constraints:
1 <= T <= 50
1 <= N, M <= 100
-10000 <= cost[i][j] <= 10000
1 <= x, y <= 100
Time limit: 1 sec
Sample Input 1:
3 4
3 4 1 2
2 1 8 9
4 7 8 1
2 3
Sample Output 1:
12
Explanation For sample input 1:
The minimum cost path will be (0, 0) -> (1, 1) -> (2, 3), So the path sum will be (3 + 1 + 8) = 12, which is the minimum of all possible paths.
Sample Input 2:
3 4
11 2 8 6
2 12 17 6
3 3 1 8
3 4
Sample Output 2:
25