Broken Calculator

Problem Statement:

There is a broken calculator. Only a few of the digits [0 to 9] and operators [+, -, *, /] are working.

A req no. needs to be formed using the working digits and the operators. Each press on the keyboard is called an operation.

= operator is always working and is used when the req no. is formed using operators.
-1 needs to be printed in case the req no. cannot be formed using the digits and the operators provided OR exceeds the max no. of operations allowed.
At no point in time during the calculation of the result, the no. should become negative or exceed 999 [0 <= calcno <= 999]

Input:

1st line contains 3 space separated nos: no. of working digits, no. of working operators, max. no of operations allowed.
2nd line contains space separated working digits.
3rd line contains space separated working operators [1 represents +, 2 represents -, 3 represents *, 4 represents /].
4th line contains the req. no to be formed.

Output:

Find the minimum required operations to form the req no.

Example:

Input 1:

Possible ways:

Case 1: 2*5*5 = -> 6 operations
Case 2: 2*25 = -> 4 operations

4 is the req Answer

Input 2:

Possible ways:
Case 1: 42 -> 2 operations (direct key in)
Case 2: 5*4*2+2 = -> 8 operations
..........some other ways

2 is the req Answer

I am not getting a proper approach to this problem.
Can someone suggest some ways to approach the problem.

Giving some more context what vish4071 said in the comments.

Set up a graph in the following way: Starting the graph with a root, and than the new node are the number you're aloud to use (for the example this is 2 and 5). And build up the graph level by level. Make each level in the following way, a new node will consist either of adding number or a operator which you're aloud to use. After each operator there cannot be another operator.

If the node has a higher value than the Target value, than kill the node (target as end note), this only works for this example (if the operators are * and +). If you would be able to use the - and / operator this is not vallid.

Do this till you find the required value, and the level (+1, due to the = operation) is you're answer.

And example of the graph is given below

for your first example:
D=0    D=1    
       5
      /
Root /
     \
      \2


D=1    D=2   d=3   d=4
            --2
           / 
          /
        (*)___5  --> reaches answer but at level 6
        /   
       /     (*)___2  --> complete
      /     /   \  5
     /     /
  2 /____25_252    --> end node
    \     \
     \     \ 
      \     
       \    225    --> end node
        \  /
         22__222   --> end node
           \            
            (*)

This is slightly better than brute forcing, maybe there is a more optimal way.