There are n students studying in the 6th grade, in group "B" of a berland secondary school. Every one of them has exactly one friend whom he calls when he has some news. Let us denote the friend of the person number i by g ( i ) . Note that the friendships are not mutual, i.e. g ( g ( i )) is not necessarily equal to i . On day i the person numbered as a i learns the news with the rating of b i ( b i ≥ 1 ). He phones the friend immediately and tells it. While he is doing it, the news becomes old and its rating falls a little and becomes equal to b i - 1 . The friend does the same thing — he also calls his friend and also tells the news. The friend of the friend gets the news already rated as b i - 2 . It all continues until the rating of the news reaches zero as nobody wants to tell the news with zero rating. More formally, everybody acts like this: if a person x learns the news with a non-zero rating y , he calls his friend g ( i ) and his friend learns the news with the rating of y - 1 and, if it is possible, continues the process. Let us note that during a day one and the same person may call his friend and tell him one and the same news with different ratings. Thus, the news with the rating of b i will lead to as much as b i calls. Your task is to count the values of res i — how many students learned their first news on day i . The values of b i are known initially, whereas a i is determined from the following formula: The first line contains two space-separated integers n and m ( 2 ≤ n , m ≤ 10 5 ) — the number of students and the number of days. The second line contains n space-separated integers g ( i ) ( 1 ≤ g ( i ) ≤ n , g ( i ) ≠ i ) — the number of a friend of the i -th student. The third line contains m space-separated integers v i ( 1 ≤ v i ≤ 10 7 ). The fourth line contains m space-separated integers b i ( 1 ≤ b i ≤ 10 7 ). Print m lines containing one number each. The i -th line should contain res i — for what number of students the first ne