\\ you can check that it correctly solves High-bits known attack, using https://pari.math.u-bordeaux.fr/gp.html
n = 167710185218043392657684711069601386011074843625572789235002071777932746636877732755140247994680284053634765181517806650050540503335551614400934944990443815044756914421473158408926693028075637765913461356212445009432046632576003592237433078605984309966451069610534724802270556433824418527511511610615749765009
pbar = 12626388512564695694240525478375224385911001084378743067485914179203720220756380636977326814427193542311162041947069243433104656238484465742105279438258176
poly = pbar + x
XX = 2^184
beta = 2^511
x = zncoppersmith(poly, n, XX, beta)[1]
gcd(n, x + pbar) == x + pbar
x+pbar