traveling salesman – Can the “closest neighbor” algorithm get arbitrarily bad in TSP?

Let’s consider the following simple algorithm for attacking the Travelling Salesman Problem:

Choose the pair of cities $(A,B)$ where $Aneq B$ and the distance between $A, B$ is minimal amongst all the distances of the cities. Start with $A$, then visit $B$, then in each step visit the nearest city not visited already, until there is no more city left.

Given $kin mathbb{N}$, is there a setting of cities such that the total distance travelled is more than $k$ times the distance travelled in an optimal solution?