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.