Problem Statement

The land of a park AtCoder is an $N\\times N$ grid with east-west rows and north-south columns. The height of the square at the $i$-th row from the north and $j$-th column from the west is given as $A_{i,j}$.

Takahashi, the manager, has decided to build a square pond occupying $K \\times K$ squares in this park.

To do this, he wants to choose a square section of $K \\times K$ squares completely within the park whose median of the heights of the squares is the lowest. Find the median of the heights of the squares in such a section.

Here, the median of the heights of the squares in a $K \\times K$ section is the height of the $(\\left\\lfloor\\frac{K^2}{2}\\right\\rfloor +1)$-th highest square among the $K^2$ squares in the section, where $\\lfloor x\\rfloor$ is the greatest integer not exceeding $x$.

Constraints

• $1 \\leq K \\leq N \\leq 800$
• $0 \\leq A_{i,j} \\leq 10^9$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$ $A_{1,1}$ $A_{1,2}$ $\\ldots$ $A_{1,N}$ $A_{2,1}$ $A_{2,2}$ $\\ldots$ $A_{2,N}$ $:$ $A_{N,1}$ $A_{N,2}$ $\\ldots$ $A_{N,N}$

Output

Print the answer.

Sample Input 1

3 2
1 7 0
5 8 11
10 4 2

Sample Output 1

4

Let $(i,j)$ denote the square at the $i$-th row from the north and $j$-th column from the west. We have four candidates for the $2 \\times 2$ section occupied by the pond: $\\{(1,1),(1,2),(2,1),(2,2)\\}, \\{(1,2),(1,3),(2,2),(2,3)\\}, \\{(2,1),(2,2),(3,1),(3,2)\\}, \\{(2,2),(2,3),(3,2),(3,3)\\}$.
When $K=2$, since $\\left\\lfloor\\frac{2^2}{2}\\right\\rfloor+1=3$, the median of the heights of the squares in a section is the height of the $3$-rd highest square, which is $5$, $7$, $5$, $4$ for the candidates above, respectively. We should print the lowest of these: $4$.

Sample Input 2

3 3
1 2 3
4 5 6
7 8 9

Sample Output 2

5