So fairly recently, i got into Kakuro and i want to create a calculator for it. the link is there for more detail on the game, but ill just go over what are the essentials i need. In kakuro, its like crosswords, except you cant use the same number in the same row/column. and all the numbers in that row/column must add up to the key value. what i need is given a key value and the amount of spaces given, what are the possible numbers that add to the key value.

so like given:

4

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where 4 is the key number and you have 2 slots, the only possible numbers that add up to it is 1 and 3. 2 and 2 doesnt count because its a repeated number.

*The Silver Phantom welcomes you*