Triangle Hunt

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.

Problem information

Author: Eryk Kopczynski

Generation: 2026-01-25T13:23:16.717Z