Problem Statement

In the gacha of a certain social game, each time you roll it $1$ time, you obtain a "Rare Character" with probability $p$ by an independent draw. In parallel with this, rolling this gacha $K$ times guarantees that you obtain a "Rare Character". Suppose you keep rolling this gacha until you obtain a "Rare Character". Compute the expected value of the number of rolls.

Answer for $T$ test cases.

Input

Line $1$ contains an integer $T$. Then, $T$ test cases follow.

Each test case is given in the following format.

$p$ $K$

The input satisfies the following constraints.

• $T$ is an integer, $1 \le T \le 1000$
• $p$ has at least $1$ and at most $3$ digits in its fractional part (including trailing $0$s), $0 \le p \le 1$
• $K$ is an integer, $1 \le K \le 500$

Output

For each test case, print the real number that is the answer as a decimal on $1$ line. There is reference data created so that its absolute or relative error from the true value is at most $10^{-10}$; the value output by the submitted program is accepted if its absolute or relative error with respect to that data is at most $10^{-5}$. Print a newline at the end.

Sample

4
0.5 2
1.0 100
0.7 5
0.002 500

1.50000000000
1.00000000000
1.42510000000
316.24437257142