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 $x$.

Input is given from Standard Input in the following format:

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

Print the answer.

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

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 2×2 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 $⌊\frac{2^2}{2}⌋+1=3$, 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.