Before revision:  This improves upon the previously best oracle complexity of O(n^2 (n + \log(R))) obtained by an elegant application of  [ Frank and Tardos, Combinatorica 1987 ] due to Dadush .
After revision:  This improves upon the previously best oracle complexity of O(n^2 (n + \log(R))) obtained by an elegant application of simultaneous diophantine approximation due to [ Frank and Tardos, Combinatorica 1987 ] due to Dadush .