John and Brus are studying string theory at the university. Brus has finished his special project - a dictionary that contains all strings of a special type. Each string in his dictionary contains exactly n occurrences of the lowercase letter 'a', m occurrences of the lowercase letter 'z', and no other letters. The strings are listed in alphabetical order.
Your task is to help John by finding the k-th (1-based) string in Brus's dictionary. If there are less than k strings in the dictionary, return an empty String instead.