In this talk, we will discuss the sum of the Schubert structure coefficients in the equivariant quantum K-theory of flag varieties G/P. We will show that the sheaf Euler characteristic of the equivariant quantum K-product of a Schubert class and an opposite Schubert class is equal to q^d, where d is the smallest degree of a rational curve joining the two Schubert varieties. Along the way, we provide a description of the smallest degree d in terms of its projections to flag varieties de fined by maximal parabolic subgroups. This is my joint work with Anders Buch, Sjuvon Chung and Leonardo Mihalcea.