The one of the coins P87919

Perhaps you have read that some problems are so classic that they barely need a statement. For this one, given a collection of $n$ coins with different values and a target amount $A$, we ask you to indicate the way to add up to $A$ by using coins of the largest possible values. In particular, a way is better than another one if the former uses more coins of the largest value; in the event of a tie, if it uses more coins of the second largest value, etc.

Input

Input consists of several cases. Each case begins with the number of coins $n$ between 1 and 100, followed by $n$ different integer numbers $v_1, \ldots, v_n$, where $1\leq v_i\leq 10000$. Finally, we have an integer number $1\leq A\leq 100000$.

Output

For every case, print in non-increasing order the necessary coins to get $A$, choosing the combination with coins of largest value in case of a tie. If there is no solution, print $-1$.