LYD loves codeforces since there are many Russian contests. In an contest lasting forT minutes there are n problems, and for the ith problem you can getai−di∗ti points, where ai indicates the initial points,di indicates the points decreased per minute (count from the beginning of the contest), andti stands for the passed minutes when you solved the problem (count from the begining of the contest). Now you know LYD can solve the ith problem in ci minutes. He can't perform as a multi-core processor, so he can think of only one problem at a moment. Can you help him get as many points as he can?
The first line contains two integers n,T(0≤n≤2000,0≤T≤5000). The second line contains n integers a1,a2,..,an(0<ai≤6000). The third line contains n integers d1,d2,..,dn(0<di≤50). The forth line contains n integers c1,c2,..,cn(0<ci≤400).
Output an integer in a single line, indicating the maximum points LYD can get.
