I have been unable to solve a problem which was given in the Zonal Informatics Olympiad 2012 paper. The problem is given below along with the link to the page where you can view the question paper and solutions.

http://www.iarcs.org.in/inoi/2012/

A toy set contains blocks showing the numbers from 1 to 9. There are plenty of blocks

showing each number and blocks showing the same number are indistinguishable. We

want to examine the number of different ways of arranging the blocks in a sequence so

that the displayed numbers add up to a fixed sum.

For example, suppose the sum is 4. There are 8 different arrangements:

1 1 1 1

1 1 2

1 2 1

1 3

2 1 1

2 2

3 1

4

The rows are arranged in dictionary order (that is, as they would appear if they were

listed in dictionary).

In each of the cases below, you are given the desired sum S and a number K. You have

to write down the Kth line when all arrangements that add up to S are written down

as described above. For instance, if S is 4 and K is 5, the answer is 2 1 1. Remember

that S may be large, but the numbers on the blocks are only from 1 to 9.

(a) S = 9, K = 156 (b) S = 11, K = 881 © S = 14, K = 4583