Dice Game Win Probability

You roll a $P$-sided die. Each face has one integer from $1$ to $P$ written on it, and every face comes up with the same probability on a single roll.

You play the following game.

• You start holding the number $K$.
• If the number you hold is $0$ or $N$, the game ends.
• Otherwise you roll the die once. If the rolled number is at most $Q$, subtract $1$ from the number you hold. If it is greater than $Q$, add $1$. Then go back to the second rule and repeat.

Write a program that computes the probability that the number you hold when the game ends is $N$.

The first line contains the integer $P$. ($1 \le P \le 100$)

The second line contains the integer $Q$. ($0 \le Q \le P$)

The third line contains the integer $N$. ($1 \le N \le 100$)

The fourth line contains the integer $K$. ($0 \le K \le N$)

Print the probability that the number you hold when the game ends is $N$. For exact judging, write the answer as a reduced fraction $a/b$ and print $(a \times b^{-1}) \bmod 1{,}000{,}000{,}007$ instead. Here $b^{-1}$ is the modular multiplicative inverse of $b$ modulo $1{,}000{,}000{,}007$. The answer exists for every input that can be given.