Problem Statement

There are $N$ kinds of snacks numbered $1$ through $N$. We have $A_i$ pieces of Snack $i$.

There are $M$ children numbered $1$ through $M$. We will distribute the pieces of snacks to these children. Here, all of the following conditions must be satisfied.

• For every kind of snack, Child $i$ gets at most $B_i$ pieces of that kind.
• Child $i$ gets at most $C_i$ pieces of snacks in total.

Find the maximum total number of pieces of snacks that can be distributed to the children under these conditions.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $1 \leq M \leq 2 \times 10^5$
• $1 \leq A_i \leq 10^{12}$
• $1 \leq B_i \leq 10^7$
• $1 \leq C_i \leq 10^{12}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
A_1 A_2 \cdots A_N
B_1 B_2 \cdots B_M
C_1 C_2 \cdots C_M

Output

Print the answer.