And where the are the phone numbers?

You are given a string s consisting of lowercase English letters and an integer k. Find the lexicographically smallest string t of length k, such that its set of letters is a subset of the set of letters of s and s is lexicographically smaller than t.

It's guaranteed that the answer exists.

Note that the set of letters is a set, not a multiset. For example, the set of letters of abadaba is {a, b, d}.

String p is lexicographically smaller than string q, if p is a prefix of q, is not equal to q or there exists i, such that pi < qi and for all j < i it is satisfied that pj = qj. For example, abc is lexicographically smaller than abcd , abd is lexicographically smaller than abec, afa is not lexicographically smaller than ab and a is not lexicographically smaller than a.

Input

The first line of input contains two space separated integers n and k (1 ≤ n, k ≤ 100 000) — the length of s and the required length of t.

The second line of input contains the string s consisting of n lowercase English letters.

Output

Output the string t conforming to the requirements above.

It's guaranteed that the answer exists.

Examples

Input

3 3
abc


Output

aca


Input

3 2
abc


Output

ac


Input

3 3
ayy


Output

yaa


Input

2 3
ba


Output

baa

Note

In the first example the list of strings t of length 3, such that the set of letters of t is a subset of letters of s is as follows: aaa, aab, aac, aba, abb, abc, aca, acb, .... Among them, those are lexicographically greater than abc: aca, acb, .... Out of those the lexicographically smallest is aca.
from functools import *
from time import time


def measure_time(fun):
    def wrapper(*args, **kwargs):
        begin = time()
        rv = fun(*args, **kwargs)
        end = time()
        print(end - begin)
        return rv
    return wrapper


def our_cache(func):
    MAX = int(1e6)
    memo = [-1]*(MAX+1)

    @wraps(func)
    def wrapper(arg):
        if memo[arg] == -1:
            memo[arg] = func(arg)
        return memo[arg]
    return wrapper


def main():
    n, k = [int(x) for x in input().split()]
    s = input()
    a = sorted(list(set([x for x in s])))
    t = []
    if k > n:
        t[:] = s
        t += (k-n)*a[0]
    else:
        for i in range(k-1, -1, -1):
            if s[i] == a[-1]:
                continue
            else:
                t[:] = s[:i]
                for j in range(0, len(a)-1):
                    if a[j] == s[i]:
                        t += a[j+1]
                t += (k-i-1)*a[0]
                break
    print("".join(t))


if __name__ == "__main__":
    main()