there is an example of BFS fail:
  - - - 2 ---- 6  - - - -- 7    - - - - -
S         / -- - - - - - /                F
  - - - 3- - - - 4 - -- - - 5  - -- - - -

going form S to F. k = 2.   BFS finds path S37F, as it is shortest.
After removing this path there is no other path from S to F.  But
choosing paths another way you could get 2.



About restrictions on vertexes - it is rather well known trick. You
double each vertex and get 2 vertexes V' and V''. Make all the graph
directed. There is an edge from V' to V'' with capacity equal  to
vertex initial capacity. All in-edges come to V' all out-edges go from
V''.


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