Flat local morphisms of rings with prescribed depth and dimension

For any pairs of integers (n,m) and (d, e) such that 0 ≤ n ≤ m, 0 ≤ d _ e, d ≤ n, e ≤ m and n -d ≤ m - e we construct a local flat ring morphism of noetherian local rings u : A → B such that dim(A) = n; depth(A) = d; dim(B) = m and depth(B) = e.