Every day, Danny buys one sweet from the candy store and eats it. The store has m types of sweets, numbered from 1 to m. Danny knows that a balanced diet is important and is applying this concept to his sweet purchasing. To each sweet type i, he has assigned a target fraction, which is a real number fi (0 < fi ≤ 1). He wants the fraction of sweets of type i among all sweets he has eaten to be roughly equal to fi. To be more precise, let si denote the number of sweets of type i that Danny has eaten, and let n = Σmi=1si. We say the set of sweets is balanced if for every i we have nfi −1<si <nfi +1. Danny has been buying and eating sweets for a while and during this entire time the set of sweets has been balanced. He is now wondering how many more sweets he can buy while still fulfilling this condition. Given the target fractions fi and the sequence of sweets he has eaten so far, determine how many more sweets he can buy and eat so that at any time the set of sweets is balanced. Input The input file contains several test cases, each of them as described below. The input consists of three lines. The first line contains two integers m (1 ≤ m ≤ 105), which is the number of types of sweets, and k (0 ≤ k ≤ 105), which is the number of sweets Danny has already eaten. The second line contains m positive integers a1, . . . , am. These numbers are proportional to f1, . . . , fm, that is, fi= ai . Σmj =1 aj It is guaranteed that the sum of all aj is no larger than 105. The third line contains k integers b1, . . . , bk (1 ≤ bi ≤ m), where each bi denotes the type of sweet Danny bought and ate on the i-th day. It is guaranteed that every prefix of this sequence (including the whole sequence) is balanced. Output For each test case, on a line by itself, display the maximum number of additional sweets that Danny can buy and eat while keeping his diet continuously balanced. If there is no upper limit on the number of sweets, display the word ‘forever’. Sample Input 65 216353 12535 64 216353 1253 Sample Output 1 forever