In a parallel universe, the most important data structure in computer science is the triangle. A triangle of size $M$ consists of $M$ rows, with the $i$-th row containing $i$ elements. Furthermore, these rows must be arranged to form the shape of an equilateral triangle. That is, each row is centred around a vertical line of symmetry through the middle of the triangle. For example, the diagram below shows a triangle of size 4:



A triangle contains sub-triangles. For example, the triangle above contains ten sub-triangles of size 1, six sub-triangles of size 2 (two of which are the triangle containing (3,1,2) and the triangle containing (4,6,1)), three sub-triangles of size 3 (one of which contains (2,2,1,1,4,2)). Note that every triangle is a sub-triangle of itself.
You are given a triangle of size $N$ and must find the sum of the maximum elements of every sub-triangle of size $K$.

The first line contains two space-separated integers $N,K\ (1≤K≤N≤3000)$.
Following this are $N$ lines describing the triangle. The i-th of these lines contains i space-separated integers $a_{i,j}\ (0≤a_{i,j}≤10^9)$, representing the i-th row of the triangle.
For 4 of the 15 available marks, $N≤1000$.

Output the integer sum of the maximum elements of every sub-triangle of size $K$.