A note on a generalization of the multiple cover formula and the simple flop

We prove a closed formula for an excess integral over the moduli space of stable maps from genus one, unmarked curves to the projective space ℙ^r of degree d for any positive integers r and d. The result generalizes the multiple cover formula for ℙ¹. We also show that any simple ℙ^r flop preserves the theory of arbitrary-genus Gromov-Witten invariants in exceptional curve classes.