  We execute Avdek's algorithm to find many algebraically overtwisted and tight
$3$-manifolds by contact $+1$ surgeries. In particular, we show that a contact
$1/k$ surgery on the standard contact $3$-sphere along any positive torus knot
with the maximum Thurston-Bennequin invariant yields an algebraically
overtwisted and tight $3$-manifold, where $k$ is a positive integer.
