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Recently, Wang introduced a novel (2, n ) region incrementing visual cryptographic scheme (RIVCS), which can gradually reconstruct secrets in a single image with multiple security levels. In RIVCS, the secret image is subdivided into multiple regions in such a way that any t shadow images, where 2 ≤ t ≤ n, can be used to reveal the (t-1) th region. However, Wang's scheme suffers from the incorrect-color problem, which the colors of reconstructed images may be reversed (i.e., the black and white are reversed). If the color of text is also the secret information, the incorrect-color problem will compromise the secret. Additionally, Wang's scheme is only suitable for the 2-out-of-n case, i.e., (k,n)-RIVCS where k=2. In this paper, we propose a general (k,n)-RIVCS, where k and n are any integers, that is able to reveal correct colors of all regions. This paper has made three main contributions: 1) our scheme is a general (k,n)-RIVCS, where k and n can be any integers; 2) the incorrect-color problem is solved; and 3) our (k,n)-RIVCS is theoretically proven to satisfy the security and contrast conditions.