  Following the work of [1], we consider six- and seven-dimensional gauged
supergravity coupled to a vector multiplet on an ansatz of
$AdS_{4,5}\times{M}_2$, respectively, where $M_2$ is a two-dimensional surface
with a Killing vector. We construct equivariantly closed forms from spinor
bilinears of Killing spinors. From the integration of equivariantly closed
forms via the Berline-Vergne-Atiyah-Bott fixed point formula, we derive the
gravitational blocks which were previously conjectured. For the construction of
equivariantly closed forms, we formulate six- and seven-dimensional gauged
supergravity in the very special geometry.
