In problems on strings one often has to find a string with some particular properties. The problem authors were reluctant to waste time on thinking of a name for some string so they called it good. A string is good if it doesn't have palindrome substrings longer than or equal to d . You are given string s , consisting only of lowercase English letters. Find a good string t with length s, consisting of lowercase English letters, which is lexicographically larger than s . Of all such strings string t must be lexicographically minimum. We will call a non-empty string s[a ... b] = s a s a + 1... s b (1 ≤ a ≤ b ≤ s) a substring of string s = s 1 s 2... s s . A non-empty string s = s 1 s 2... s n is called a palindrome if for all i from 1 to n the following fulfills: s i = s n - i + 1 . In other words, palindrome read the same in both directions. String x = x 1 x 2... x x is lexicographically larger than string y = y 1 y 2... y y , if either x y and x 1 = y 1, x 2 = y 2, ... , x y = y y , or there exists such number r (r x, r y), that x 1 = y 1, x 2 = y 2, ... , x r = y r and x r + 1 y r + 1 . Characters in such strings are compared like their ASCII codes.

输入描述:

The first line contains integer d (1 ≤ d ≤ s).The second line contains a non-empty string s, its length is no more than 4·105 characters. The string consists of lowercase English letters.

输出描述:

Print the good string that lexicographically follows s, has the same length and consists of only lowercase English letters. If such string does not exist, print "Impossible" (without the quotes).