There are a number of ways to shuffle a deck of cards. Riffle shuffle is one such example. The following is how to perform riffle shuffle.

There is a deck of *n* cards. First, we divide it into two decks; deck A which consists of the top half of it and deck B of the bottom half. Deck A will have one more card when *n* is odd.

Next, *c* cards are pulled from bottom of deck A and are stacked on deck C, which is empty initially. Then *c* cards are pulled from bottom of deck B and stacked on deck C, likewise. This operation is repeated until deck A and B become empty. When the number of cards of deck A(B) is less than *c*, all cards are pulled.
Finally we obtain shuffled deck C. See an example below:

- A single riffle operation where n = 9, c = 3 for given deck [0 1 2 3 4 5 6 7 8] (right is top) - Step 0 deck A [4 5 6 7 8] deck B [0 1 2 3] deck C [] - Step 1 deck A [7 8] deck B [0 1 2 3] deck C [4 5 6] - Step 2 deck A [7 8] deck B [3] deck C [4 5 6 0 1 2] - Step 3 deck A [] deck B [3] deck C [4 5 6 0 1 2 7 8] - Step 4 deck A [] deck B [] deck C [4 5 6 0 1 2 7 8 3] shuffled deck [4 5 6 0 1 2 7 8 3]

This operation, called riffle operation, is repeated several times.

Write a program that simulates Riffle shuffle and answer which card will be finally placed on the top of the deck.

The input consists of multiple data sets. Each data set starts with a line containing two positive integers *n*(1 ≤ *n* ≤ 50) and *r*(1 ≤ *r* ≤ 50); *n* and *r* are the number of cards in the deck and the number of riffle operations, respectively.

*r* more positive integers follow, each of which represents a riffle operation. These riffle operations are performed in the listed order. Each integer represents *c*, which is explained above.

The end of the input is indicated by EOF. The number of data sets is less than 100.

For each data set in the input, your program should print the number of the top card after the shuffle. Assume that at the beginning the cards are numbered from 0 to *n*-1, from the bottom to the top. Each number should be written in a sparate line without any superfluous characters such as leading or following spaces.

9 1 3 9 4 1 2 3 4

3 0

Source: University of Aizu Programming Contest
, Aizu-Wakamatsu, Japan, 2008

(extra problem for 2008)

(extra problem for 2008)