D. Klyukalo
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Klyukalo consists of $$$N$$$ parts, each with its own standard — the $$$i$$$-th part should weigh $$$s_i$$$ grams. If there is a klyukalo where the $$$i$$$-th part weighs $$$a_i$$$ grams, its deviation can be calculated using the formula $$$\frac{|a_i - s_i|}{s_i}$$$. The deviation of the entire construction is calculated using the formula $$$\Sigma \frac{|a_i - s_i|}{s_i}$$$, which is the sum of the deviations of each part. The allowable deviation of the klyukalo according to the standard is $$$K$$$.

You are given a klyukalo. In one minute, you can either increase the weight of one part by $$$1$$$ gram or decrease the weight of one part by $$$1$$$ gram. What is the minimum time required to bring the given klyukalo to the standard with a deviation of no more than $$$K$$$?

Input

The first line contains two integers $$$N$$$ and $$$K$$$ — the number of parts in the klyukalo and the allowable deviation $$$(1 \le N \le 10^5, 0 \le K \le 10^9)$$$.

The second line contains $$$N$$$ integers $$$s_i$$$ — the weights of the parts in the standard $$$(1 \le s_i \le 10)$$$.

The third line contains $$$N$$$ integers $$$a_i$$$ — the weights of the parts in the given klyukalo $$$(1 \le a_i \le 10^9)$$$.

Output

Output the minimum number of minutes required to bring the given klyukalo to the standard with a deviation of no more than $$$K$$$.

Example
Input
3 1
1 2 1
2 4 3
Output
3
Note

In the example, you can reduce the weight of the first and third parts to the standard.