There has already been a long line in front of the cafeteria before the school bell rang.

When the cafeteria opens, everyone in the queue rushes to one of the n windows in the cafeteria at a speed close to the speed of light, forming a new n queue.

This process follows the following rules:

1. Each person rushes to the ith () window independently with a probability of 1/n;
2. If A is in front of B at the beginning, and A and B rush to the same window, then A is still in front of B.

Playf is now ranked m in the team, which means that there are m-1 people ahead of Playf. Playf wants to know the expectation of rank of him in the new queue after the cafeteria opens.

One line, two integers n and m.
1<=n,m<=1e9

One line, a floating point number, indicates the expectation of Playf' rank in the new queue. At least accurate to 1e-6.

2 3

2.00000000

There are 8 possibilities with equal probability

2 4

2.50000000