Filling a rectangle with blocks

You have an unlimited number of blocks of each size $1 \times N$, $2 \times N$, $\dots$, $N \times N$. Use them to fill a rectangle of $N$ rows and $M$ columns with no gaps.

A block can be turned by $90^\circ$. That is, a $k \times N$ block can be placed as $k$ rows by $N$ columns, or as $N$ rows by $k$ columns. Blocks must not overlap and must not stick out of the rectangle.

Two fillings count as different if any cell is covered by a block of a different position or shape. Print the number of fillings modulo $1999$.

The first line contains $N$ and $M$, separated by a space. ($1 \le N \le 100$, $1 \le M \le 10^4$)

Print the number of fillings modulo $1999$ on one line.