Given a weighted digraph $G=(V,E)$, where each edge is associated with a weight (could be positive, negative, or zero). We define the weight of a path to be the sum of the weights along this path.
The question: given two vertices $s,t$, decide whether there is a (not necessarily simple) path from $s$ to $t$ such that the weight of the path is 0.
It is not very difficult to see that this problem is in NP. I am wondering whether there is a polynomial time algorithm, or it is NP-hard.