F. Workout plan
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Alan decided to get in shape for the summer, so he created a precise workout plan to follow. His plan is to go to a different gym every day during the next N days and lift $X[i]$ grams on day $i$. In order to improve his workout performance at the gym, he can buy exactly one pre-workout drink at the gym he is currently in and it will improve his performance by $A$ grams permanently and immediately. In different gyms these pre-workout drinks can cost different amounts $C[i]$ because of the taste and the gym's location but its permanent workout gains are the same. Before the first day of starting his workout plan, Alan knows he can lift a maximum of $K$ grams. Help Alan spend a minimum total amount of money in order to reach his workout plan. If there is no way for him to complete his workout plan successfully output $-1$.

Input

The first one contains two integer numbers, integers $N$ $(1 \leq N \leq 10^5)$ and $K$ $(1 \leq K \leq 10^5)$ – representing number of days in the workout plan and how many grams he can lift before starting his workout plan respectively. The second line contains $N$ integer numbers $X[i]$ $(1 \leq X[i] \leq 10^9)$ separated by a single space representing how many grams Alan wants to lift on day $i$. The third line contains one integer number $A$ $(1 \leq A \leq 10^9)$ representing permanent performance gains from a single drink. The last line contains $N$ integer numbers $C[i]$ $(1 \leq C[i] \leq 10^9)$ , representing cost of performance booster drink in the gym he visits on day $i$.

Output

One integer number representing minimal money spent to finish his workout plan. If he cannot finish his workout plan, output -1.

Examples
Input
5 10000
10000 30000 30000 40000 20000
20000
5 2 8 3 6

Output
5

Input
5 10000
10000 40000 30000 30000 20000
10000
5 2 8 3 6

Output
-1

Note

First example: After buying drinks on days 2 and 4 Alan can finish his workout plan. Second example: Alan cannot lift 40000 grams on day 2.