Roll a fair m-sided die repeatedly until a roll comes out strictly greater than k. Return the expected sum of every roll, the stopping one included.

Split it in two:

• each roll that fails to stop you is uniform on $1..k$, and you expect $k/(m-k)$ of them
• the final roll is uniform on $k+1..m$

Input

m = 6
k = 4

Output

10.5