Ceil and Floor functions on fractions

Question

Is floor(a/k)=ceil(a/(k+1)) always where a>=1 and k>=1? I have tried using the fact that

x-1<ceil(a/b)<=x if ceil(a/b)=x  and 
x<=floor(a/b)<x+1 if floor(a/b)=x

but unable to reach any conclusion