Euphony#3009
In the Latin alphabet, there are letters, six of which are vowels: "a", "e", "i", "o", "u", and "y". The others are consonants. According to research by British scientists, it has been discovered that words with too many consonants, or long sequences of consecutive consonants, are difficult to pronounce and unpleasant to the ear. More precisely, a word is considered euphonious if the ratio of the number of consonants to the number of vowels does not exceed a threshold , and the word does not contain a fragment consisting of more than consecutive consonants. To make a word euphonious, you are allowed to insert letters at any position in the word.
Write a program that transforms the given word into a euphonious one.
The first line contains a positive real number with at most two digits after the decimal point, and a natural number . Both numbers do not exceed 10^6. The second line contains a word of no more than 10^5 lowercase Latin letters.
Output the shortest possible euphonious word that can be obtained from the given word by inserting letters. Output the answer in a single line.
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