Represent $N$ as the sum of exactly $K$ distinct positive integers

Question

You are given two integers $N$ and $K$. Find all ways to represent $N$ as the sum of exactly $K$ distinct positive integers $x_1,x_2, \ldots,x_K$ — in other words.

$xi_>0$ for each valid $i$;

$x_i \neq x_j$ for each valid $i \neq j$;

$x_1+x_2+ \ldots +x_K=N$

For Example : $N=15$ and $K=3$

Answer should be: $1+2+12, 1+3+11, 1+4+10, 1+5+9, 1+6+8, 2+3+10, 2+4+9, 2+5+8, 2+6+7, 3+4+8, 3+5+7, 4+5+6$

How to code to generate these combinations in any language?

Answer 1

Are you currently participating in SnackDown Round 1B, Then you should not ask this question before the competition ends, you are violating the codechef code of conduct for the competition.