Elimination of contestants from a live IQ contest on a TV channel is decided in phases.

Initially at phase 0, N contestants, where N = 2ⁿ , n < 10 , are selected through a special online IQ contest in which a total of M (M > N) contestants participate. The contestants are identified by distinct registration numbers 1, 2,..., M . The selected contestants are ranked distinctly from 1 to N according to their performance in the online contest. They are qualified to participate in the live contest.

In the p^th phase, p = 1, 2,..., n, K_p contestants participate in the live contest, where K_p = 2^n-p+1 . On the basis of response to questions presented during the show, K_p/2 of K_p contestants are ranked distinctly from 1 to K_p/2 . These K_p/2 contestants qualify to participate in the next phase. At the n^th phase there are only two contestants and the one selected at this phase is the winner of the contest.

You are required to write a program that identifies the winner of the contest, given the following information:

• INFO_1: Registration numbers of N contestants who are selected through the online IQ contest, in order of the rank in the online IQ contest, and
• INFO_2: A total of N - 1 qualified contestants in different phases; K₂ in phase 1, K₃ in phase 2, ... , and K_n+1 in phase n . Qualified contestants of different phases appear in order of phases, i.e., phase 1, phase 2, ... , phase n . Further, qualified contestants in a phase, say phase p , appear in the order of the rank in the phase, i.e., the rank in phase p . A qualified contestant of a phase, say phase p , is identified by his/her rank in the previous phase, i.e., in phase p - 1 .

Input 

Input may contain multiple test cases. For each case there are two input lines.

The first line gives N integers representing INFO_1 while the second line gives N - 1 integers representing INFO_2.

In each input line integers are separated by space. The input terminates with a line containing 0 as input.

Output 

For each test case there is only one output line. The line prints the registration number of the winner of the contest.

Sample Input 

23 18 6 20
4 2 2
29 57 4 33 5 12 16 18
7 1 5 3 2 1 1
0

Sample Output 

18
29