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;
typedef long long ll;
const int INF = (1<<30);
const ll INFLL = (1ll<<60);
const ll MOD = (ll)(1e9+7);

#define l_ength size

void mul_mod(ll& a, ll b){
	a *= b;
	a %= MOD;
}

void add_mod(ll& a, ll b){
	a = (a<MOD)?a:(a-MOD);
	b = (b<MOD)?b:(b-MOD);
	a += b;
	a = (a<MOD)?a:(a-MOD);
}

vector<string> v;

int main(void){
	int n,i,k,p=1,q,m=0;
	string s,t,ans;
	cin >> n >> k; --k;
	cin >> s;
	t = s;
	reverse(s.begin(),s.end());
	t += s;
	reverse(s.begin(),s.end());
	for(i=0; i<n; ++i){
		v.push_back(t.substr(i,n));
	}
	sort(v.begin(),v.end());
	while(p<n && v[0][p-1] == v[0][p]){
		++p;
	}
	q = p;
	while(k){
		q *= 2;
		if(q > n){
			break;
		}
		--k;
	}
	q -= p;
	for(i=0; i<q; ++i){
		if(m<n){
			ans.push_back(v[0][0]);
			++m;
		}
	}
	for(i=0; i<n; ++i){
		if(m<n){
			ans.push_back(v[0][i]);
			++m;
		}
	}
	cout << ans << endl;
	return 0;
}
