Sunday Coding

Yeongseon is entering the online programming contest "Sunday Coding".

While the contest runs, the participants are split into $R$ rooms and each room holds $S$ participants, so there are $R \times S$ participants in total. The rooms are numbered from $1$ to $R$.

Nobody ties, so once the contest ends every participant receives a distinct rank from $1$ (the overall win) to $R \times S$.

The winner of a room is the participant with the best rank in that room.

After the contest Yeongseon writes down the rank of each room winner in room order, which gives a sequence of length $R$. The $i$-th number of the sequence is the rank of the winner of room $i$.

Given $R$ and $S$, write a program that counts the different sequences that can be produced this way.

The first line contains $R$ and $S$, separated by a space. ($1 \le R, S \le 100$)

On the first line, print the number of different sequences that can be produced, modulo 1,000,000,007.

For $R = 2$ and $S = 1$ there are two rooms with one participant each, so the sequence is either $(1, 2)$ or $(2, 1)$.

For $R = 2$ and $S = 2$ the sequences that can be produced are $(1, 2)$, $(2, 1)$, $(1, 3)$, $(3, 1)$. Neither $(2, 3)$ nor $(1, 4)$ is ever possible.