Is { k^2 * r mod 1 | k is integer} dense in [0,1]?

Let r be an irrational number.
I know and can prove that { k* r mod 1 | k is integer} is dense in
[0,1].
My question is -- Is { (k^2) * r mod 1 | k is integer } dense in
[0,1] ?

Thanks!
.