Triangle Hunt X03259

Statement

Measharan Bees have built a regular triangle made of hexagonal honeycells. Each honeycell contains some amount of honey.

Now, we want to sell exactly $M$ units of honey. For this, we have to cut out a triangle which contains exactly $M$ units. We only consider regular triangles which have a horizontal edge here.

In the picture above, there are two triangles, each of which contains 10 honeycells with 100 units of honey each. All other triangles contain a number other than 1000 (there would be a third solution if the cell with 15 units contained 10 units).

Input

The first line of input contains two numbers $N$ and $M$ ( $1 \leq N \leq 500, 1 \leq M \leq 50000$ ).

The $i$ -th of the following numbers contains $i$ numbers, each of them in range from $0$ to $10000$ . The picture above corresponds to the sample.

Output

Output the number of triangles which contain exactly $M$ units of honey.

Public test cases

Input

10 1000
10
10 10
10 10 10
10 10 10 10
10 100 100 100 100
10 10 100 100 100 10
10 10 15 100 100 10 100
10 10 10 10 100 10 100 100
10 10 10 10 10 10 100 100 100
10 10 10 10 10 10 100 100 100 100

Output

Information

Author: Eryk Kopczynski
Language: English
Official solutions: Unknown.
User solutions: C++