Congruence for Lattice Path Models with Filter Restrictions and Long Steps

We derive a path counting formula for two-dimensional lattice model with filter restrictions in the presence of long steps, source and target points which are situated near filters. This solves problem finding an explicit multiplicities modules tensor product decomposition T(1)⊗N Uq(sl2) divided powers, where q is root unity. Combinatorial treatment this calls definition congruence regions models, properties explored paper.