Indian National Olympiad in Informatics

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Online Programming Contest, 4-5 December 2004

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Basic Division

Problem 2: Find the Numbers, (K Narayan Kumar, CMI)

This is a rather simple problem to describe. You will be given three numbers S, P and k. Your task is to find if there are integers n₁, n₂,...,n_k such that n₁ + n₂ +...+ n_k = S, n₁ * n₂ * ... * n_k = P. If such integers exist, print them out. If no such sequence of integers exist, then print "NO".

For example if S=11, P=48 and k=3 then 3, 4 and 4 is a solution. On the other hand, if S=11, P=100 and k=3, there is no solution and you should print "NO".

Input format

A single line with three integers S, P and k.

Output format

A single word "NO" or a seqence of k integers n₁, n₂,..., n_k on a single line. (The n_i's must add up to S and their product must be P).

Test data

You may assume that 1 ≤ k ≤ 4, 1 ≤ S ≤ 1000 and 1 ≤ P ≤ 1000.

Example

We now illustrate the input and output formats using some examples.

Sample input 1:

11 48 3

Sample output 1:

3 4 4

Sample input 2:

11 100 3

Sample output 2:

NO