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In the world of Mathematics, there are ordinary numbers and there are special numbers. The special numbers are Transformers. The transformers are of two types - Autobots and Decepticons. Autobots have the task of saving the number-kind from the evil intentions of Decepticons.
A number C is said to be equivalent to another number D if C%k = D%k, where k is a given parameter.
The Transformers are called so because of their special ability to transform to something else. Now, given a value Q, a transformer N wishes to transform to another value P such that P is equivalent to Q.
However, like all mortal beings, they too have restrictions, they can only take some particular transformations.
The following transformations are allowed
N -> N + a
N -> N - b
N -> N * c
N -> N % d
You have to report minimum number of steps to transform to such a value P (which is equivalent to Q) using the above transformations, or print -1 if it is impossible to do so.
First line contains T, the number of test cases. T lines follow, each containing 7 space separated integers, N, a, b, c, d, k, q.
The output consists of T lines. Each line contains the output of the corresponding test case, i.e., the minimum number of transformations required or -1, if transformation is not possible.
2 10 3 2 5 5 4 12 5 1 2 3 4 9 14
1 <= T <= 1000 1 <= N,a,b,c,d,k,Q <= 1000
For test case 1:
1. Take 10 modulo 5 -> 0 which equals 12 modulo 4
For test case 2: No operations requires as 5 modulo 9 = 14 modulo 9
modulo operation is defined here. It is commonly implemented as
% operator in many programming languages.
All test cases are generated randomly.
|Time Limit:||1 sec|
|Source Limit:||50000 Bytes|
|Languages:||C, CPP 4.9.2, GO, JAVA|
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