Takahashi has a string S of length N consisting of lowercase English letters. On this string, he will perform the following operation K times:

* Let T be the string obtained by reversing S, and U be the string obtained by concatenating S and T in this order.
* Let S' be some contiguous substring of U with length N, and replace S with S'.



Among the strings that can be the string S after the K operations, find the lexicographically smallest possible one.

Constraints

* 1 \leq N \leq 5000
* 1 \leq K \leq 10^9
* |S|=N
* S consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:


N K
S


Output

Print the lexicographically smallest possible string that can be the string S after the K operations.

Examples

Input

5 1
bacba


Output

aabca


Input

10 2
bbaabbbaab


Output

aaaabbaabb
#include <bits/stdc++.h>
using namespace std;
 
const int Maxn = 10005;
int n, k, mini = 0x3f3f3f3f, maxi, cnt[Maxn], ct;
string S[Maxn], str, tmp;
int main()
{
	scanf("%d%d", &n, &k);
	cin >> str;
	for (int i = 0; i < n; i++)
		str += str[n - i - 1];
	for (int i = 0; i < 2 * n; i++)
		mini = min(mini, str[i] - 'a');
	for (int i = 0; i < 2 * n; i++)
	{
		if (str[i] - 'a' == mini) cnt[i] = cnt[i - 1] + 1;
		else cnt[i] = 0;
		maxi = max(maxi, cnt[i]);
	}
	int limit = min(n, maxi * ((1 << (min(15, k) - 1)) - 1));
	for (int i = 0; i < n; i++)
	{
		tmp = "";
		if (cnt[i + n] != maxi) continue;
		for (int j = i + n; j > i + limit; j--)
			tmp += str[j];
		S[++ct] = tmp;
	}
	sort(S + 1, S + 1 + ct);
	for (int i = 0; i < limit; i++)
		putchar(mini + 'a');
	for (int i = limit; i < n; i++)
		putchar(S[1][i - limit]);
	return 0;
}
