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 bisect import bisect_right

a = list(map(lambda x: int(x), input().split(' ')))

n, k = a[0], a[1]

s = input()

res = ''

s_min = min(s)
s_max = max(s)

st = sorted(set(s))

def find_gt(a, x):
    'Find leftmost value greater than x'
    i = bisect_right(a, x)
    if i != len(a):
        return a[i]
    raise ValueError

if n < k:
    for i, l in enumerate(s):
        if i >= k:
            break

        res += l

    for i in range(0, k - n):
        res += s_min

elif n > k:
    found = False
    for l in reversed(s[0:k]):
        if found:
            res += l
        elif l == s_max:
            res += s_min
        else:
            res += find_gt(st, l)
            found = True

    res = ''.join(reversed(res))
else:
    found = False
    for l in reversed(s):
        if found:
            res += l
        elif l == s_max:
            res += s_min
        else:
            res += find_gt(st, l)
            found = True

    res = ''.join(reversed(res))

print(res)



