Dirichlet box principle

Question

In a more quantified version: for natural numbers $k$ and $m$, if $n = km + 1$ objects are distributed among $m$ sets, then the pigeonhole principle asserts that atleast one of the sets will contain at least $k + 1$ objects. (from wikipedia) Now why is 'atleast' there? Only one set should contain only $k+1$ objects, as $n$ is just one more than $k$ items (are being contained by $m$ sets) , i.e. $n=km+1$

Answer 1

Let $k=3$ and $m=2$ so that $n=7$. Then one possible arrangement is $(5,2)$, but neither of these is $k+1=4$.