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 <cstdio>
char s[10000];

int main()
{
	int n, k; scanf("%d%d%s", &n, &k, s);
	// reverse & concat
	for (int i = 0; i < n; ++i)
		s[n + i] = s[n - i - 1];
	// find min suffix
	int min = 0;
	for (int tmp = 1; tmp < n; ++tmp)
		for (int i = 0; i < n; ++i)
			if (s[min + i] != s[tmp + i])
			{
				if (s[min + i] > s[tmp + i])
					min = tmp;
				break;
			}
	char *str = &s[min];
	// find prefix length of <str[0]>
	int len = 1;
	while (len < n)
		if (str[len] == str[0])
			++len;
		else 
			break;
	// double the length for each k
	int max = len;
	while (--k)
	{
		max *= 2;
		if (max > n)
		{
			max = n;
			break;
		}
	}
	// print answer
	for (int i = 0; i < max; ++i)
		printf("%c", str[0]);
	for (int i = max; i < n; ++i)
		printf("%c", str[len + i - max]);
	printf("\n");
}