Pebble game on graph

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Consider the problem whose instance is a directed graph with the selected vertex V and k of 'pebbles'. We can in any order, perform the following elemental steps:

  • on top of x we can put a pebble, if at a given moment are pebbles at all predecessors, of which leads edge to the x
  • pebble placed on vertex you can remove (and reuse later).

The question is whether there exists a sequence of steps in which we put a pebble on the specified vertex v.

Can anyone prove that the problem is in PSPACE, please?