Description: You are playing a famous computer game (that just works) where you have various skills you can level up. Today, you focused on the "Smithing" skill. Your tactic is obvious: forging weapons from ingots and then melting them back to return the materials partially. For simplicity, every time you create an item, you get $$$1$$$ experience point, and every time you melt an item, you also get $$$1$$$ experience point. There are $$$n$$$ classes of weapons you can forge and $$$m$$$ types of metal ingots. You can create one weapon of the $$$i$$$-th class, spending $$$a_i$$$ ingots of metal of the same type. Melting a weapon of the $$$i$$$-th class (which you crafted earlier) returns you $$$b_i$$$ ingots of the type of metal it was made of. You have $$$c_j$$$ metal ingots of the $$$j$$$-th type, and you know that you can craft a weapon of any class from any metal type. Each combination of a weapon class and a metal type can be used any number of times. What is the maximum total amount of experience you can earn by crafting and melting weapons? Input Format: The first line contains two integers $$$n$$$ and $$$m$$$ ($$$1 \le n, m \le 10^6$$$) — the number of weapon classes and metal types. The second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le 10^6$$$), where $$$a_i$$$ is the number of ingots you need to forge one weapon of the $$$i$$$-th class. The third line contains $$$n$$$ integers $$$b_1, b_2, \dots, b_n$$$ ($$$0 \le b_i < a_i$$$), where $$$b_i$$$ is the number of ingots you return by melting one weapon of the $$$i$$$-th class you forged earlier. The fourth line contains $$$m$$$ integers $$$c_1, c_2, \dots, c_m$$$ ($$$1 \le c_j \le 10^9$$$) — the number of ingots you have of the corresponding metal type. Output Format: Print one integer — the maximum total experience points you can gain by repeatedly forging and melting weapons. Note: In the first example, you can do the following: 1. craft one weapon of the $$$1$$$-st class from the $$$1$$$-st type of metal, spending $$$9$$$ ingots; 2. melt that weapon, returning $$$8$$$ ingots of the $$$1$$$-st metal type; 3. again, craft and melt one weapon of the $$$1$$$-st class from the $$$1$$$-st metal type; 4. craft and melt one weapon of the $$$3$$$-rd class from the $$$1$$$-st metal type; 5. craft and melt one weapon of the $$$3$$$-rd class from the $$$3$$$-rd metal type; 6. craft and melt one weapon of the $$$4$$$-th class from the $$$1$$$-st metal type; 7. craft and melt one weapon of the $$$5$$$-th class from the $$$3$$$-rd metal type;