Problem Statement

There are $N$ magical floors on the $xy$-plane, and the $i$-th ($1 \le i \le N$) magical floor occupies the range $H_{i-1} \le y < H_{i}$. Here, $0 = H_0 < H_1 < \cdots < H_N = H$ holds. The speed of movement on this plane depends on the location: on the $i$-th magical floor, it takes time $A_i$ to travel a distance of $1$. You want to move from $(0,\ 0)$ to $(X,\ 0)$ through the part of this plane with $0 \le y < H$. Find the minimum time required for the move.
Answer $T$ test cases.

Input

$T$

$N\ X$
$H_1\ H_2\ \cdots \ H_N$
$A_1\ A_2\ \cdots \ A_N$

(Constraints)
All inputs are integers
$1 \le N \le 100$
$1 \le X \le 10^9$
$0 < H_1 < H_2 < \cdots < H_N \le 10^9$
$0 \le A_i \le 10^9$

Output

Output the minimum time required to move from $(0,\ 0)$ to $(X,\ 0)$.
Print a newline at the end.
Your answer is considered correct if its absolute or relative error from the correct answer is at most $10^{-8}$.
It can be proved that the minimum value always exists under the constraints of this problem.

Sample

3
2 2
1 2
2 1
2 5
2 3
1 0
2 4
1 2
2 1

4
4
7.464101615137754