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This paper increases the flexibility of generalized histogram shifting-based reversible data hiding (HS-RDH). An RDH method modifies an original image to hide data to the image, and the method not only extracts the hidden data but also restores the original image from the distorted image which conveys the hidden data. A generalized HS-RDH method increases (or decreases) particular pixel values in an original image by (q - 1), based on its tonal distribution, to hide q-ary data symbols, whereas an ordinary HS-RDH method shifts a part of the histogram by one to embed binary symbols. This paper introduces an adaptive binary-to-q-ary watermark converter and a tonal distribution analysis to increase conveyable hidden data size, whereas a conventional generalized HS-RDH method with an arithmetic decoder-based converter cannot always convert the extracted q-ary strings to original binary strings correctly and the other method embeds q̂-symbols instead of q-ary symbols where q̂ is a power of two equal to or less than q. In addition, histogram packing technique is introduced in this paper to further increase q. Experimental results show the effectiveness of the proposed method.