Twilight Sparkle was playing Ludo with her friends Rainbow Dash, Apple Jack and Flutter Shy. But she kept losing. Having returned to the castle, Twilight Sparkle became interested in the dice that were used in the game.
The dice has m faces: the first face of the dice contains a dot, the second one contains two dots, and so on, the m-th face contains m dots. Twilight Sparkle is sure that when the dice is tossed, each face appears with same probability. Also she knows that each toss is independent from others.
There is n + 1 cells in total, number from 0 to n, Twilight Sparkle race her token from 0 to n according to die rolls. The game end once she move to n or over it. Help Twilight Sparkle calculated the probability she end the game exactly at n.
Input
Input contains multiple test cases (less than 200).
For each test case, only one line contains two integers $m$ and $n$ ($1 \leq m, n \leq 10^9$).
Output
For each case, output the corresponding result, rounded to 5 digits after the decimal point.
