Children matches are not toys! - 2#2659
There are matches on the table. Two players take turns. On each turn, a player may take at least one, but no more than matches. The player who takes the last match wins.
As you may already know, with optimal play, the first player generally has a much better chance of winning than the second player. Therefore, Vasya and Masha agreed that Masha will always go first, and Vasya will choose the maximum number of matches that can be taken in a single move. What is the smallest number that Masha should choose so that she can guarantee a win no matter what natural number up to Vasya chooses? According to their agreement, the number picked by Masha must be at least twice as large as the number picked by Vasya.
The first line contains the number — the number of test cases. Each of the following lines contains a number — the maximum value that Vasya may choose for .
1 \le T \le 1000, K \le 2 \cdot 10^9.
For each test case, output the corresponding value of in a separate line. It is guaranteed that the number of test cases in each test does not exceed .
Example 1