YSACODE discuss3

Description

You are hosting a party and do not have room to invite all of your friends. You use the following unemotional mathematical method to determine which friends to invite.

Number your friends 1,2,…,K and place them in a list in this order. Then perform m rounds. In each round, use a number to determine which friends to remove from the ordered list.

The rounds will use numbers r1,r2,…,rm. In round i remove all the remaining people in positions that are multiples of ri (that is, ri,2ri,3ri,…) The beginning of the list is position 1.

Output the numbers of the friends that remain after this removal process.

Input

The first line of input contains the integer

(1≤K≤100)(1≤K≤100). The second line of input contains the integer

(1≤m≤10)(1≤m≤10), which is the number of rounds of removal. The next

mmlines each contain one integer. The

ithith of these lines

(1≤i≤m)(1≤i≤m) contains

riri

(2≤ri≤100)(2≤ri≤100) indicating that every person at a position which is multiple of

riri should be removed.

Output

The output is the integers assigned to friends who were not removed. One integer is printed per line in increasing sorted order.

Sample Input Copy

Sample Output Copy

Source/Category