  We give a formula in terms of Young diagrams to calculate the minimum
positive integer $d$ such that $q^d$ appears in the quantum product of two
Schubert classes for the submaximal isotropic Grassmannians in Types B and C.
We do this by studying curve neighborhoods. We compute curve neighborhoods in
several combinatorial models including $k$-strict partitions and a set of
partitions where their inclusion is compatible with the Bruhat order.
