Journey with Pigs

Farmer John runs a pig farm near town A and wants to visit a friend who lives in town B. On the road to town B he passes n small villages, so he decides to make some money along the way. He sets out with n pigs and sells exactly one pig in each village he passes.

Pork prices differ from village to village: in the j-th village people buy pork at p_j rubles per kilogram. The distance from town A to the j-th village along the road is d_j kilometers.

The pigs have different weights. Transporting one kilogram of pork over one kilometer of road costs t rubles in extra fuel. So carrying a pig of weight w over a distance d costs w·d·t rubles, while selling it in the j-th village earns w·p_j rubles; the net earning from that pig is therefore w·(p_j − d_j·t) rubles.

John must sell exactly one pig in each village — that is, he assigns pigs to villages one-to-one and sells them all. Choose the assignment that maximizes the sum of the net earnings and report the maximum total amount of money John can earn.

The first line contains two integers n (1 ≤ n ≤ 1000) and t (1 ≤ t ≤ 10^9). The second line contains n integers w_i (1 ≤ w_i ≤ 10^9), the weights of the pigs. The third line contains n integers d_j (1 ≤ d_j ≤ 10^9), the distances from town A to the villages. The fourth line contains n integers p_j (1 ≤ p_j ≤ 10^9), the pork prices in the villages.

Print a single integer: the maximum total amount of money John can earn when he sells exactly one pig in each village. Because every pig must be sold, this value can be negative.