Anuj has challenged Arun to climb P stairs but at only in powers of X and Y. Now Arun being a lazy guy wants to do this in minimum number of steps possible. So he has asked for your help to calculate the minimum number of steps he requires to take for climbing P stairs ( 1 step = some power of X or Y stairs ).

Input:
The first line of input contains an integer T denoting the number of test cases. Then T test cases follow. Each test case contains 3 space separated integers P, X and Y, where P is the number of stairs to be climbed.

Output:
Corresponding to each test case, in a new line, print the number of steps that Arun needs to take to climb P stairs in powers of X & Y. If fit is not possible print -1.

Constraints:
1<=T<=200
1<=P,X,Y<=10^5

Example: Input:
2
15 2 3
19 4 3

Output:
3
2

Explanation:
In the first case, we can make 15 by (8,4,3) or (9,3,3) both takes 3 steps.
In the second case, we can make 19 by (16,3) which is 2 steps.