K. Keen on Rösti
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

The world's problems have worsened, with hunger prevailing, even in Polymensa. With only one scoop of Rösti per day, Polymensa queue becomes battleground for survival. Oli, lost in his research, skipped the Probability Lecture as usual and needs your help to determine his expected loss for the day.

There are $$$n$$$ students, including Oli, who form a queue for the single scoop of Rösti at Polymensa. The fate of the student at the front(first place of the queue) is determined by a magical ladle. There's a probability $$$\frac{a}{b}$$$ that the ladle scoops out Rösti. If not, the student pays a coin as a penalty and moves to the end(n-th place) of the queue while everyone else shifts one place forward. The process continues, with the student at the front having a probability of $$$\frac{a}{b}$$$ to receive Rösti. If unsuccessful, the student moves to the end of the queue, and so on.

When someone gets the single scoop of Rösti this whole process stops.

Calculate the expected amount of coins spent by Oli, who initially occupies the $$$k$$$-th place in the queue, modulo $$$10^9+7$$$.

Input

Input contains two lines.

In the first line, you are given $$$n$$$, representing the number of students and $$$k$$$, representing the place of Oli in the queue $$$(1 \leq k \leq n \leq 10^{9})$$$

In the second line you are given $$$a$$$ and $$$b$$$, such that the probability of the magical ladle scooping out the Rösti is $$$\frac{a}{b}$$$ $$$(1 \leq a \leq b \leq 10^{9})$$$

Output

Print one integer the expected amount of coins spent by Oli, taken modulo $$$10^9+7$$$.

The required expected value can be represented as an irreducible fraction $$$\frac{p}{q}$$$. You have to print the value $$$p \cdot q^{-1} \mod 1000000007$$$. Note that any valid input in this problem is co-prime to $$$10^9+7$$$.

Examples
Input
3 1
1 2
Output
571428576
Input
5 2
1 3
Output
725118489
Input
1000000000 1000000000
1000000000 1000000000
Output
0
Note

In the first test, the answer is $$$\frac{4}{7}$$$. There are $$$3$$$ students waiting, and Oli is first in the queue. The person at the front has probability of $$$\frac{1}{2}$$$ getting Rösti.

Note that $$$4 \cdot 7 ^{-1} = 571428576 \mod (10^9 + 7)$$$.

In the second test, the answer is $$$108/211$$$. There are $$$5$$$ students waiting, and Oli is second in the queue. The person at the front has probability of $$$\frac{1}{3}$$$ getting Rösti.

In the third test, the person at the front of the queue will get the dish on the first attempt. So, poor Oli doesn't even get a chance to experience the magical ladle and spends $$$0$$$ coins.