You are given a graph G, and the problem is to test whether there is a cycle of length at most 1000 or not. Is the problem in P or in NP? Give a formal proof for your answer. A 'Yes' or 'No' answer is...

You are given a graph G, and the problem is to test whether there is a cycle of length at most 1000 or not.

Is the problem in P or in NP?Give a formal proof for your answer. A 'Yes' or 'No' answer is not sufficient to get a non-zero mark on this question.