Income Tax

A little-known but ambitious company is building a large project to make it easier for ordinary citizens of Flatland to track their budgets. You are part of this project and must write a program that computes the income tax, which is the tax levied on earned income.

The tax rules are fairly complex and consist of $k + 1$ parts:

• If income $X$ is less than $U_1$, the tax is $p_1$ percent, that is, $X \cdot \frac{p_1}{100}$.
• If $X$ is at least $U_1$ and less than $U_2$, the tax on the first $U_1$ is $p_1$ percent, and the tax on the remaining amount is $p_2$ percent. So the total tax is $U_1 \cdot \frac{p_1}{100} + (X - U_1) \cdot \frac{p_2}{100}$.
• $\ldots$
• If $X$ is at least $U_k$, the tax from the earlier parts stays the same, and the remainder $X - U_k$ is taxed at $p_{k+1}$ percent. The total tax is $U_1 \cdot \frac{p_1}{100} + (U_2 - U_1) \cdot \frac{p_2}{100} + \ldots + (X - U_k) \cdot \frac{p_{k+1}}{100}$.

Given income $X$, compute the income tax.

The first line contains two integers $X$ and $k$ ($0 \le X \le 10^9$, $1 \le k \le 100$). The second line contains $k$ integers $U_1, U_2, \ldots, U_k$ ($1 \le U_1 < U_2 < \ldots < U_k \le 10^9$). The third line contains $k + 1$ integers $p_1, p_2, \ldots, p_k, p_{k+1}$ ($0 \le p_1 \le p_2 \le \ldots \le p_{k+1} \le 100$).

Print the income tax that an honest citizen of Flatland must pay after earning $X$ units of Flatland currency, on a single line. Print the answer with exactly two digits after the decimal point.