Holidays

On a planet in the Alpha Centauri system, a week has $A$ days and a year has $B$ days. Years are numbered with consecutive positive integers: $1, 2, 3, \ldots$. Years numbered $C_1, C_2, \ldots, C_N$ are leap years and have $(B+1)$ days. In a year, the days numbered $D_1, D_2, \ldots, D_M$ are holidays. If a holiday falls on day $(B+1)$ of the year, it is observed only in leap years. The first day of the first year is the first day of the week.

A resident of the planet has decided to take a new job. Under the employment contract, he will hold this job for $E$ days, starting from the first day of year 1. By the contract, he may choose one day of the week (from 1 to $A$) as his day off. Holidays are also counted as non-working days. The resident wants to choose his day off so that during the contract period he has the maximum number of non-working days.

Write a program that finds this day of the week and computes the corresponding number of non-working days.

The first line contains $A$ and $B$, the number of days in a week and in a non-leap year, separated by a space ($1\le A \le 2500$, $1\le B \le 10000$). The second line contains $N$, the number of leap years, and the third line contains the numbers $C_1, C_2, \ldots, C_N$ of the leap years in increasing order ($0\le N \le 5000$, $1 \le C_1 < C_2 < \ldots < C_N \le 10^7$). The next line contains $M$, the number of holidays in a year, and the line after it contains $D_1, D_2, \ldots, D_M$ in increasing order ($1 \le D_1 < D_2 < \ldots < D_M \le B+1$). The last line contains $E$ ($1\le E \le 10^9$). The contract lasts no more than $10^7$ years.

Output two numbers separated by a space: the number of the day of the week that is most advantageous to take as a day off, and the corresponding number of non-working days during the contract period. If there are several answers, output any of them.