The only difference between the easy and the hard versions is constraints.

A subsequence is a string that can be derived from another string by deleting some or no symbols without changing the order of the remaining symbols. Characters to be deleted are not required to go successively, there can be any gaps between them. For example, for the string "abaca" the following strings are subsequences: "abaca", "aba", "aaa", "a" and "" (empty string). But the following strings are not subsequences: "aabaca", "cb" and "bcaa".

You are given a string s consisting of n lowercase Latin letters.

In one move you can take any subsequence t of the given string and add it to the set S. The set S can't contain duplicates. This move costs n - |t|, where |t| is the length of the added subsequence (i.e. the price equals to the number of the deleted characters).

Your task is to find out the minimum possible total cost to obtain a set S of size k or report that it is impossible to do so.

Input

The first line of the input contains two integers n and k (1 ≤ n ≤ 100, 1 ≤ k ≤ 10^{12}) — the length of the string and the size of the set, correspondingly.

The second line of the input contains a string s consisting of n lowercase Latin letters.

Output

Print one integer — if it is impossible to obtain the set S of size k, print -1. Otherwise, print the minimum possible total cost to do it.

Examples

Input


4 5
asdf


Output


4


Input


5 6
aaaaa


Output


15


Input


5 7
aaaaa


Output


-1


Input


10 100
ajihiushda


Output


233

Note

In the first example we can generate S = { "asdf", "asd", "adf", "asf", "sdf" }. The cost of the first element in S is 0 and the cost of the others is 1. So the total cost of S is 4.
import java.util.*;
import java.io.*;
public class Solution implements Runnable 
{  
    
    class Pair implements Comparable <Pair>
    {
        long x,y;
        Pair(long x,long y)
        {
            this.x=x;
            this.y=y; 
        }
        public int compareTo(Pair p)
        {
            return Long.compare(x,p.x);
        }
    }
    
    public static void main(String[] args)
    {
        new Thread(null, new Solution(), "rev", 1 << 29).start();
    }

    public void run()
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Task solver = new Task();
        solver.solve(1,in,out);
        out.close();
    }
    
    class Task
    { 
        
        void solve(int testNumber, InputReader in, PrintWriter out)
        { 
            int n=in.nextInt();
            long k=in.nextLong();
            String s=in.nextString();
            long [][]dp=new long[n+1][n+1];
            int []l=new int[26];
            for(int i=0;i<=n;i++)
            {
                for(int j=0;j<=n;j++)
                {
                   if(j>i)
                       continue;
                   if(j==0)
                   dp[i][j]=1;
                   else
                   {
                       dp[i][j]=dp[i-1][j]+dp[i-1][j-1];
                       if(l[s.charAt(i-1)-'a']!=0)
                           dp[i][j]-=dp[l[s.charAt(i-1)-'a']-1][j-1];
                   }
                }
                if(i>0)
                    l[s.charAt(i-1)-'a']=i;
            }
            long ans=0;
            for(int j=n;j>=0;j--)
            {
                if(dp[n][j]>=k)
                {
                    ans+=(k*(n-j));
                    k=0;
                    break;
                }
                else
                {
                    ans+=(dp[n][j]*(n-j));
                    k-=dp[n][j];
                }
            }
            if(k>0)
                out.println("-1");
            else
                out.println(ans);
        }
    }
    
}
  class InputReader 
{
    private InputStream stream;
    private byte[] buf = new byte[8192];
    private int curChar, snumChars;
    private SpaceCharFilter filter;
 
    public InputReader(InputStream stream) 
    {
        this.stream = stream;
    }
 
    public int snext() 
    {
        if(snumChars==-1)
            throw new InputMismatchException();
        if(curChar>=snumChars)
        {
            curChar=0;
            try 
            {
                snumChars = stream.read(buf);                
            } 
            catch(IOException e) 
            {
                throw new InputMismatchException();
            }
            if(snumChars<=0)
                return -1;
        }
        return buf[curChar++];
    }
 
    public int nextInt()
    {
        int c = snext();
        while(isSpaceChar(c))
            c=snext();
        int sgn=1;
        if(c=='-')
        {
            sgn = -1;
            c = snext();
        }
        int res=0;
        do
        {
            if(c<'0' || c>'9')
                throw new InputMismatchException();
            res*=10;
            res+=c-'0';
            c=snext();
            }while(!isSpaceChar(c));
        return res * sgn;
    }
 
    public long nextLong()
    {
        int c = snext();
        while(isSpaceChar(c))
            c=snext();
        int sgn=1;
        if(c=='-')
        {
            sgn=-1;
            c=snext();
        }
        long res=0;
        do{
            if (c<'0' || c>'9')
                throw new InputMismatchException();
            res*=10;
            res+=c-'0';
            c=snext();
        }while (!isSpaceChar(c));
        return res * sgn;
    }
 
    public int[] nextIntArray(int n)
    {
        int a[]=new int[n];
        for(int i=0; i<n; i++)
            a[i]=nextInt();
        return a;
    }
 
    public String nextString()
    {
        int c=snext();
        while(isSpaceChar(c))
            c=snext();
        StringBuilder res=new StringBuilder();
        do{
            res.appendCodePoint(c);
            c = snext();
        }while (!isSpaceChar(c));
        return res.toString();
    }
 
    public boolean isSpaceChar(int c)
    {
        if(filter != null)
            return filter.isSpaceChar(c);
        return c==' ' || c=='\n' || c=='\r' || c=='\t' || c==-1;
    }
 
    public interface SpaceCharFilter
    {
        public boolean isSpaceChar(int ch);
    }
}