Q:

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

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?

A:

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