# Evaluate Division

Posted: 9 Jan, 2021

Difficulty: Moderate

#### You are given an array of pairs of strings 'EQUATIONS', and an array of real numbers 'VALUES'. Each element of the 'EQUATIONS' array denotes a fraction where the first string denotes the numerator variable and the second string denotes the denominator variable, and the corresponding element in 'VALUES' denotes the value this fraction is equal to.

#### You are given ‘Q’ queries, and each query consists of two strings representing the numerator and the denominator of a fraction. You have to return the value of the given fraction for each query. Return -1 if the value cannot be determined.

##### Example :

```
'EQUATIONS' = { {“a”, ”s”} , {“s”, “r”} }
'VALUES' = { 1.5, 2 }
queries = { {“a”, “r” } }
For the above example (a / s) = 1.5 and (s / r) = 2 therefore (a / r) = 1.5 * 2 = 3.
```

##### Input Format :

```
The first line contains a single integer ‘T’ denoting the number of test cases. The test cases are as follows.
The first line of each test case contains two integers, ‘N’ and ‘Q,’ separated by a single space denoting the number of the equations and the number of queries, respectively.
The second line of each test case contains ‘N’ strings denoting the numerator variable of the 'EQUATIONS'.
The third line of each test case contains ‘N’ strings denoting the denominator variable of the 'EQUATIONS'.
The fourth line of each test case contains ‘N’ real numbers denoting the 'VALUE' of each fraction.
The fifth line of each test case contains ‘Q’ strings denoting the numerator variable for each query.
The sixth line of each test case contains ‘Q’ strings denoting the denominator variable for each query.
```

##### Output Format :

```
For each test case, return the value of the fraction up to 5 decimal places or -1 if the value of the fraction cannot be determined. All values are separated by a single space.
Your output will be considered correct if the relative error does not exceed 10^(-6).
```

##### Note :

```
You don’t need to print anything, It has already been taken care of. Just implement the given function.
```

##### Constraints :

```
1 <= T <= 50
1 <= N <= 100
1 <= Q <= 100
1 <= |S| <= 10
0.0 < values[i] <= 100.0
Where '|S|' denotes the length of the variables, and 'VALUES[i]' denotes the value of the i’th equation.
Time limit: 1 sec
```