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>
#define be(v) (v).begin(),(v).end()
#define pb(q) push_back(q)
typedef long long ll;
using namespace std;
const ll mod=1000000007, INF=mod*mod*3LL;
#define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl;

int main() {
    cin.tie(0);
    cout.tie(0);
    ios::sync_with_stdio(false);
    string s;
    int n, k;
    cin >> n >> k >> s;
    string t = s;
    reverse(be(t));
    s += t;
    string u = s.substr(0, n);
    for(int i=1;i<=n;i++) u = min(u, s.substr(i, n));
    int x = 1;
    while(x < u.length() && u[0] == u[x]) x++;
    int y = x;
    k--;
    if(k > 17) y = n;
    else y <<= k;
    string ans = "";
    while(ans.length() < n && y > 0) y--, ans += u[0];
    ans += u.substr(x, n - ans.length());
    cout << ans << endl;
    return 0;
}
