B'A popular reality show is recruiting a new cast for the third season! n candidates numbered from 1 to n have been interviewed. The candidate i has aggressiveness level l_i , and recruiting this candidate will cost the show s_i roubles. The show host reviewes applications of all candidates from i=1 to i=n by increasing of their indices, and for each of them she decides whether to recruit this candidate or not. If aggressiveness level of the candidate i is strictly higher than that of any already accepted candidates, then the candidate i will definitely be rejected. Otherwise the host may accept or reject this candidate at her own discretion. The host wants to choose the cast so that to maximize the total profit. The show makes revenue as follows. For each aggressiveness level v a corresponding profitability value c_v is specified, which can be positive as well as negative. All recruited participants enter the stage one by one by increasing of their indices. When the participant i enters the stage, events proceed as follows: It is allowed to select an empty set of participants (to choose neither of the candidates). The host wants to recruit the cast so that the total profit is maximized. The profit is calculated as the total revenue from the events on stage, less the total expenses to recruit all accepted participants (that is, their total s_i ). Help the host to make the show as profitable as possible. The first line contains two integers n and m ( 1 <= n, m <= 2000 ) -- the number of candidates and an upper bound for initial aggressiveness levels. The second line contains n integers l_i ( 1 <= l_i <= m ) -- initial aggressiveness levels of all candidates. The third line contains n integers s_i ( 0 <= s_i <= 5000 ) -- the costs (in roubles) to recruit each of the candidates. The fourth line contains n + m integers '...