  Define a ``truncation'' $r_{t}(p)$ of a polynomial $p$ in
$\{x_1,x_2,x_3,...\}$ as the polynomial with all but the first $t$ variables
set to zero. In certain good cases, the truncation of a Schubert or
Grothendieck polynomial may again be a Schubert or Grothendieck polynomial. We
use this phenomenon to give subtraction-free formulae for certain Schubert
structure constants in $K(Flags({\mathbb C}^n))$, in particular generalizing
those from [Kogan '00] in which only cohomology was treated, and from [Buch
`02] on the Grassmannian case. The terms of the answer are computed using
``marching'' operations on permutation diagrams.
