  In (1+1)-d CFTs, the 4-point function on the plane can be mapped to the
pillow geometry and thereby crossing symmetry gets translated into a modular
property. We use these modular features to derive a universal asymptotic
formula for OPE coefficients in which one of the operators is averaged over
heavy primaries. The coarse-grained heavy channel then reproduces features of
the gravitational 2-to-2 S-matrix which has black holes as their intermediate
states.
