K-th Substring

You are given a string s. Among the different substrings of s, print the K-th lexicographically smallest one.

A substring of s is a string obtained by taking out a non-empty contiguous part in s. For example, if s = ababc, a, bab and ababc are substrings of s, while ac, z and an empty string are not. Also, we say that substrings are different when they are different as strings.

Let X = x_{1}x_{2}...x_{n} and Y = y_{1}y_{2}...y_{m} be two distinct strings. X is lexicographically larger than Y if and only if Y is a prefix of X or x_{j} > y_{j} where j is the smallest integer such that x_{j} \neq y_{j}.

Constraints

• 1 ≤ |s| ≤ 5000
• s consists of lowercase English letters.
• 1 ≤ K ≤ 5
• s has at least K different substrings.

Input

Input is given from Standard Input in the following format:

s K

Output

Print the K-th lexicographically smallest substring of K.

Examples

Input

aba 4

Output

b

Input

atcoderandatcodeer 5

Output

andat

Input

z 1

Output

z

inputFormat

Input

Input is given from Standard Input in the following format:

s K

outputFormat

Output

Print the K-th lexicographically smallest substring of K.

Examples

Input

aba 4

Output

b

Input

atcoderandatcodeer 5

Output

andat

Input

z 1

Output

z

样例

aba
4

b