How to make a loop that goes thru an array of ints to..?

Check if an addition of any combination of those numbers could equal to a few certain numbers?
For example I have numbers 164, 211, 225, 258, 266, 313. And I have array with 61, 55, 55, 55, 55, 47, 47, 47, 47, 69, 69, 120, 28, 91. I want to check if by adding a combination of the numbers from the second array I can possibly get one of the numbers from the first array and if so, which of the numbers I need to add. How do I do this? Note that a number in the array can only be used once.
My head is about to explode from to implement this. My basic idea is to first add all combinations of any 2 integers in the array, then add all combinations of any 3 integers in the array, etc until you add all of the numbers in the array.
Of course there is a more efficient way of doing this but this seems the simplest to me.
PS: I am also not sure about whether I can overwrite an array with a new array with new size each time thru a loop. But it doesn't give me an error.
This is as far as I got so far. When I got to the identical 2 loops one inside each other I realized I am doing something wrong and it can all be done with 1 big loop. But I mean the deepness of loops in this case depends on how many ints we are currently adding so how would that work?

    /*Simply compares the integer to see if it equals to one of the desired results*/

    public static boolean desiredResult(int input)

    {

        boolean desiredResult = false;

        if (input == 164 || input == 211 || input == 225 || input == 258 || input == 266 || input == 313)

        {

            desiredResult = true;

        }

        return desiredResult;

    }

    public static void main(String[] args)

    {

        int[] additions = {61, 55, 55, 55, 55, 47, 47, 47, 47, 69, 69, 120, 28, 91}; //the array of numbers to be added

        int[] currentAdd; //the numbers that are currently being added

        int currentAddIndex; //the index of the array of numbers that are being added currently

        for (int howManyIntsAdded=2; howManyIntsAdded<additions.length; howManyIntsAdded++) //how many integers to be added together 2-13

        {

            currentAdd = new int[howManyIntsAdded]; //array of numbers currently being added depending on howManyIntsAdded

            for (int firstIndex=0; firstIndex<additions.length-(howManyIntsAdded-1); firstIndex++) //determine the first number to add

            {

                currentAddIndex = 0;

                currentAdd[currentAddIndex] = additions[firstIndex];

                currentAddIndex++;

                for (int secondIndex=firstIndex+1; secondIndex<additions.length-(howManyIntsAdded-2); secondIndex++) //second number to add

                {

                    currentAdd[currentAddIndex] = additions[secondIndex];

                    currentAddIndex++;

                }

            }

        }

    }

Any help would be extremely appreciated. I am totally lost here.