Tom and Ray are facing off in an epic game of chance!

The game is played with a running "score" and a special coin that has a positive integer printed on each side. Tom and Ray take turns flipping the coin. After each flip, the number that lands face-up is added to the score.

Ray wins if the score ever becomes exactly ~s~ at any point during the game. Tom wins if the score passes ~s~.

What is the probability that Ray will win the game?

Input

The first line contains two integers ~a~ and ~b~ ~(1 \leq a, b \leq 10^8)~, the numbers on each side of the coin.

The second line contains an integer ~s~ ~(1 \leq s \leq 10^5)~, the score Ray must reach to win.

Output

Output the probability that Ray will win the game, correct to ~4~ decimal places.

Examples

Input 1

1 2
2

Output 1

0.7500

Ray can win in ~2~ ways:

• If a ~2~ is flipped on the first turn (~1/2~ probability).
• If a ~1~ is flipped on the first turn, and again on the second (~1/4~ probability).

Therefore, he has a ~1/4 + 1/2 = 3/4~ probability of winning.

Input 2

2 3
5

Output 2

0.5000

Ray can win in ~2~ ways:

• If a ~2~ is flipped on the first turn, and a ~3~ is flipped on the second (~1/4~ probability).
• If a ~3~ is flipped on the first turn, and a ~2~ is flipped on the second (~1/4~ probability).

Therefore, he has a ~1/4 + 1/4 = 1/2~ probability of winning.

Input 3

10 10
5

Output 3

0.0000

There is no way for Ray to win.