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.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		PrintWriter out = new PrintWriter(outputStream);
		InputReader in = new InputReader(inputStream);
		
//		for(int i=4;i<=4;i++) {
//			InputStream uinputStream = new FileInputStream("leftout.in");
//			String f = i+".in";
//			InputStream uinputStream = new FileInputStream(f);
//			InputReader in = new InputReader(uinputStream);
//			PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("leftout.out")));
			Task t = new Task();
			t.solve(in, out);
			out.close();			
//		}
	}	
	
	static class Task {
		int times = 0;
		public void solve(InputReader in, PrintWriter out) throws IOException {
//			//int xxx = in.nextInt();
//			//while(xxx-->0) {
//				int n = in.nextInt();
//				int k = in.nextInt();
//				int a[] = in.readIntArray(n);
//				int b[] = in.readIntArray(n);
//				ArrayList<Integer>[] g = new ArrayList[n];
//				for(int i=0;i<n;i++) g[i] = new ArrayList<Integer>();
//				for(int i=0;i<n-1;i++) {
//					g[a[i]-1].add(a[i+1]-1);
//					g[b[i]-1].add(b[i+1]-1);
//				}
//				boolean vis[] = new boolean[n];
//				int lvl[] = new int[n];
//				int low[] = new int[n];
//				int hash[] = new int[n];
//				times = 0;
//				dfs(a[0]-1,g,vis,low,lvl,hash);
//				int cycles = 0; int cycle_nodes = 0;
//				DSU dsu = new DSU(n);
//				for(int i=0;i<n;i++) {
//					if(hash[low[i]]<i) {
//						dsu.union(hash[low[i]], i);
//					}else {
//						dsu.union(i,hash[low[i]]);
//					}
//				}
//				HashMap<Integer,Integer> s = new HashMap<Integer,Integer>();
//				for(int i=0;i<n;i++) {
//					int tmp = dsu.find(i);
//					s.put(tmp, s.getOrDefault(tmp, 0)+1);
//					//low[i] = s.get(dsu.find(i));
//				}
//				for(int i:s.keySet()) {
//					if(s.get(i)>1) {
//						cycles++;
//						cycle_nodes+=s.get(i);
//					}
//				}
//				if(k==3) {
//					//Dumper.print("here");
//				}
//				if(n-cycle_nodes+cycles>=k) {
//					System.out.println("YES");
//					//out.println("YES");
//					int temp [] = new int[n];
//					for(int i=0;i<n;i++) temp[i] = low[a[i]-1];
//					for(int i=1;i<n;i++) {
//						if(temp[i]>temp[i-1]+1) temp[i] = temp[i-1]+1;				
//						if(temp[i]>=k) temp[i] = temp[i-1];								
//					}
//					for(int i=0;i<n;i++) {
//						low[a[i]-1] = temp[i]; 
//					}
//					for(int i=0;i<n;i++) {
//						System.out.print((char)('a'+low[i]));
//						//out.print((char)('a'+low[i]));
//					}
//					System.out.println();
//					//out.println();
//				}
//				else {
//					System.out.println("NO");
//					//out.println("NO");	
//				}
//			//}
			int n = in.nextInt();
			long k = in.nextLong();
			char[] arr = in.next().toCharArray();
			long dp[][][] = new long[n+1][n+1][26];
			dp[0][n][0] = 1;
			for(int i=1;i<=n;i++) {
				int x = (int)(arr[i-1]-'a');
				dp[1][i][x] = 1;
				for(int j=0;j<26;j++) {
					if(j!=x) dp[1][i][j] += dp[1][i-1][j];
				}
			}
			for(int i=2;i<=n;i++) {//length
				for(int j=i;j<=n;j++) {//end point
					int x = (int)(arr[j-1]-'a');
					for(int p=0;p<26;p++) {//26 chars
						dp[i][j][x] += dp[i-1][j-1][p];						
					}		
					for(int p=0;p<26;p++) {
						if(dp[i][j][p]==0) dp[i][j][p]+=dp[i][j-1][p];
					}
				}
			}
			long cost = 0;
			int p = n; int q = 0;
			while(p>=0&&k>0) {
				cost+= Math.min(k, dp[p][n][q])*(n-p);
				k-=dp[p][n][q];
				q++;
				p-=q/26;
				q%=26;
			}
			out.println(k>0?-1:cost);
		}
		
		class pair implements Comparable<pair>{
			int num, like, dlike;
			public pair(int b, int c, int d) {
				num=b;like=c;dlike=d;
			}
			public int compareTo(pair x) {
				return x.dlike-this.dlike;
			}
		}		
		
	    public int maxLength(List<String> arr) {
	    	int n = arr.size();
	    	int w[] = new int[n];
	        int[][] a = new int[n][26];
	        for(int i=0;i<n;i++) {
	        	String tmp = arr.get(i);
	        	w[i] = tmp.length();
	        	for(int j=0;j<tmp.length();j++) {
	        		a[i][tmp.charAt(j)-'a']++;
	        		if(a[i][tmp.charAt(j)-'a']>1) w[i]=0;
	        	}
	        }
	        boolean g[][] = new boolean[n][n];	       
	        for(int i=0;i<n;i++) {
	        	for(int j=i+1;j<n;j++) {
	        		boolean flag = false;
	        		for(int k=0;k<26;k++) {
	        			if(a[i][k]!=0&&a[j][k]!=0) flag = true; 
	        		}
	        		if(!flag) g[i][j] = g[j][i] = true;
	        	}
	        }
	        int max = 0;
	        for(int i=0;i<(1<<n);i++) {
	        	boolean flag = true;
	        	for(int j=0;j<n;j++) {if((i&(1<<j))==0) continue;
	        		if((i&(1<<j))==0||!flag) continue;
	        		for(int k=j+1;k<n;k++) {
	        			if((i&(1<<k))==0||!flag) continue;
	        			if(!g[j][k]) flag = false;
	        		}
	        	}
	        	if(!flag) continue;
	        	//Dumper.print(i);
	        	int s = 0;
	        	for(int j=0;j<n;j++) if((i&(1<<j))==(1<<j)) s+=w[j];
	        	if(s>max) max = s;
	        }
	        return max;
	    }

		
		int dfs(int cur, ArrayList<Integer>[] g, boolean vis[], int low[], int[] lvl, int hash[]) {
			lvl[cur] = low[cur] = times;
			hash[times] = cur;
			times++;
			int reach = low[cur];
			vis[cur] = true;
			for(int to:g[cur]) {
				if(vis[to]) {
					reach = Math.min(reach, low[to]);
				}else {
					int tmp = dfs(to,g,vis,low,lvl,hash);
					reach = Math.min(reach, tmp);
				}
			}
			if(reach<low[cur]) low[cur] = reach;
			return low[cur];
		}
		class edge implements Comparable<edge>{
			int f,t,l,s;
			public edge(int a, int b, int c) {
				if(a<b){
					f=a;t=b;
				}else {
					f=b;t=a;
				}
				l=c;
			}
			@Override
			public int compareTo(edge t) {
				return this.l-t.l;
			}			
		}


			    	
		List<List<Integer>> convert(int arr[][]){
			int n = arr.length;
			List<List<Integer>> ret = new ArrayList<>();
			for(int i=0;i<n;i++) {
				ArrayList<Integer> tmp = new ArrayList<Integer>();
				for(int j=0;j<arr[i].length;j++) tmp.add(arr[i][j]);
				ret.add(tmp);
			}
			return ret;
		}
		
	    public int maximumSum(int[] arr) {
	        int n = arr.length;
	        int dp[][] = new int[n][2];
	        dp[0][0] = arr[0];
	        int ret = arr[0];
	        for(int i=1;i<n;i++) {
	        	dp[i][0] = dp[i-1][0]>=0?(dp[i-1][0]+arr[i]):arr[i];
	        	int t1 = dp[i-1][0];
	        	int t2 = (dp[i-1][1]<0?0:dp[i-1][1])+arr[i];
	        	dp[i][1] = Math.max(t1,t2);
	        	ret = Math.max(ret,Math.max(dp[i][0], dp[i][1]));
	        } 
	        return ret;
	    }		
	    public List<Integer> findNumOfValidWords(String[] words, String[] puzzles) {
	        List<Integer> ret = new ArrayList<Integer>();
	        HashMap<Integer,Integer>[] mp = new HashMap[26];
	        for(int i=0;i<26;i++) mp[i] = new HashMap<Integer,Integer>();
	        //String p = "abcdz";
	        //Dumper.print(enc(p));
	        for(int i=0;i<words.length;i++) {
	        	int v = enc(words[i]);
	        	for(int j=0;j<words[i].length();j++) {
	        		mp[words[i].charAt(j)-'a'].put(v, 1);
	        	}
	        }
	        for(int i=0;i<puzzles.length;i++) {
	        	int n = puzzles[i].length();
	        	int t = 0;
	        	for(int j=1;j<1<<(n-1);j++) {
	        		int v = 0;
	        		for(int k=0;k<6;k++) {
	        			if((j&(1<<k))!=0) {
	        				v|=(1<<(puzzles[i].charAt(k)-'a'));
	        			}
	        		}
	        		v|=(1<<(puzzles[i].charAt(0)-'a'));   		
	        		//t+=search(v,mp[puzzles[i].charAt(0)-'a']);
	        	}
	        	ret.add(t);
	        }
	        return ret;
	    }	
	    int search(int x, HashMap<Integer,Integer> mp, HashSet<Integer> hs) {
	    	if(mp.containsKey(x)) return mp.get(x);
	    	if(x==0) return 0;
	    	int v = 0;
	    	for(int i=0;i<7;i++) {
	    		if((x&(1<<i))!=0) {
	    			int t = x;
	    			t^=(1<<i);
	    			if(!hs.contains(t)) {
	    				hs.add(t);
	    				v+=search(t,mp,hs);	    				
	    			}
	    		}
	    	}
	    	mp.put(x, v);	    	
	    	return v;
	    }
	    int enc(String x) {
	    	char[] arr = x.toCharArray();
	    	int v = 0;
	    	for(int i=0;i<arr.length;i++) {
	    		v|=1<<(arr[i]-'a');
	    	}
	    	return v;
	    }
		
		public class TreeNode {
			int val;
			TreeNode left;
			TreeNode right;
			TreeNode(int x) { val = x; }
		}
	
		public int GCD(int a, int b) {
		   if (b==0) return a;
		   return GCD(b,a%b);
		}
		public long GCD(long a, long b) {
			   if (b==0) return a;
			   return GCD(b,a%b);
			}		
	}
	
	
    static class ArrayUtils {
        static final long seed = System.nanoTime();
        static final Random rand = new Random(seed);

        public static void sort(int[] a) {
            shuffle(a);
            Arrays.sort(a);
        }

        public static void shuffle(int[] a) {
            for (int i = 0; i < a.length; i++) {
                int j = rand.nextInt(i + 1);
                int t = a[i];
                a[i] = a[j];
                a[j] = t;
            }
        }

    }	
	static class BIT{
		int arr[];
		int n;
		public BIT(int a) {
			n=a;
			arr = new int[n];
		}
		int sum(int p) {
			int s=0;
			while(p>0) {
				s+=arr[p];
				p-=p&(-p);
			}
			return s;
		}
		void add(int p, int v) {
			while(p<n) {
				arr[p]+=v;
				p+=p&(-p);
			}
		}
	}
	static class DSU{
		int[] arr;
		int[] sz;
		public DSU(int n) {
			arr = new int[n];
			sz = new int[n];
			for(int i=0;i<n;i++) arr[i] = i;
			Arrays.fill(sz, 1);
		}
		public int find(int a) {
			if(arr[a]!=a) arr[a] = find(arr[a]);
			return arr[a];
		}
		public void union(int a, int b) {
			int x = find(a);
			int y = find(b);
			if(x==y) return;
			arr[y] = x;
			sz[x] += sz[y];
		}
		public int size(int x) {
			return sz[find(x)];
		}
	}	
	static class MinHeap<Key> implements Iterable<Key> {
		private int maxN;
		private int n;
		private int[] pq;
		private int[] qp;
		private Key[] keys;
		private Comparator<Key> comparator;
		
		public MinHeap(int capacity){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
		}
		
		public MinHeap(int capacity, Comparator<Key> c){
			if (capacity < 0) throw new IllegalArgumentException();
			this.maxN = capacity;
			n=0;
			pq = new int[maxN+1];
			qp = new int[maxN+1];
			keys = (Key[]) new Object[capacity+1];
			Arrays.fill(qp, -1);
			comparator = c;
		}			
		public boolean isEmpty()	{ return n==0; 	}
		public int size()			{ return n;		}
		public boolean contains(int i) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        return qp[i] != -1;
		}	
		public int peekIdx() {
	        if (n == 0) throw new NoSuchElementException("Priority queue underflow");
	        return pq[1];		
		}	
		public Key peek(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			return keys[pq[1]];
		}
		public int poll(){
			if(isEmpty()) throw new NoSuchElementException("Priority queue underflow");
			int min = pq[1];
			exch(1,n--);
			down(1);
			assert min==pq[n+1];
			qp[min] = -1;
			keys[min] = null;		
			pq[n+1] = -1;
			return min;
		}
	    public void update(int i, Key key) {
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (!contains(i)) {
	        	this.add(i, key);
	        }else {
	        	keys[i] = key;
	        	up(qp[i]);
	        	down(qp[i]);
	        }
	    }	
		private void add(int i, Key x){
	        if (i < 0 || i >= maxN) throw new IllegalArgumentException();
	        if (contains(i)) throw new IllegalArgumentException("index is already in the priority queue");
	        n++;
	        qp[i] = n;
	        pq[n] = i;
	        keys[i] = x;
	        up(n);
		}
		private void up(int k){
			while(k>1&&less(k,k/2)){
				exch(k,k/2);
				k/=2;
			}
		}
		private void down(int k){
			while(2*k<=n){
				int j=2*k;
				if(j<n&&less(j+1,j)) j++;
				if(less(k,j)) break;
				exch(k,j);
				k=j;
			}
		}
		
		public boolean less(int i, int j){
	        if (comparator == null) {
	            return ((Comparable<Key>) keys[pq[i]]).compareTo(keys[pq[j]]) < 0;
	        }
	        else {
	            return comparator.compare(keys[pq[i]], keys[pq[j]]) < 0;
	        }
		}

		public void exch(int i, int j){
	        int swap = pq[i];
	        pq[i] = pq[j];
	        pq[j] = swap;
	        qp[pq[i]] = i;
	        qp[pq[j]] = j;
		}

		@Override
		public Iterator<Key> iterator() {
			// TODO Auto-generated method stub
			return null;
		}
	}  	

    private static class InputReader
    {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int zcurChar;
        private int znumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
            this.stream = stream;
        }

        public int read()
        {
            if (znumChars == -1)
                throw new InputMismatchException();
            if (zcurChar >= znumChars)
            {
            	zcurChar = 0;
                try
                {
                    znumChars = stream.read(buf);
                } catch (IOException e)
                {
                    throw new InputMismatchException();
                }
                if (znumChars <= 0)
                    return -1;
            }
            return buf[zcurChar++];
        }

        public int nextInt()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String nextString()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do
            {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public double nextDouble()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.')
            {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.')
            {
                c = read();
                double m = 1;
                while (!isSpaceChar(c))
                {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, nextInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }

        public long nextLong()
        {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-')
            {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do
            {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c)
        {
            if (filter != null)
                return filter.isSpaceChar(c);
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public String next()
        {
            return nextString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
        public int[] readIntArray(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }        
    }    

	static class Dumper {
		static void print_int_arr(int[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_char_arr(char[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_double_arr(double[] arr) {
			for (int i = 0; i < arr.length; i++) {
				System.out.print(arr[i] + " ");
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(int[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print_2d_arr(boolean[][] arr, int x, int y) {
			for (int i = 0; i < x; i++) {
				for (int j = 0; j < y; j++) {
					System.out.print(arr[i][j] + " ");
				}
				System.out.println();
			}
			System.out.println();
			System.out.println("---------------------");
		}

		static void print(Object o) {
			System.out.println(o.toString());
		}

		static void getc() {
			System.out.println("here");
		}
	}
}