Problem: You are given two strings s and t consisting of lowercase Latin letters. The length of t is 2 (i.e. this string consists only of two characters).

In one move, you can choose any character of s and replace it with any lowercase Latin letter. More formally, you choose some i and replace s_i (the character at the position i) with some character from 'a' to 'z'.

You want to do no more than k replacements in such a way that maximizes the number of occurrences of t in s as a subsequence.

Recall that a subsequence is a sequence that can be derived from the given sequence by deleting zero or more elements without changing the order of the remaining elements.

Input

The first line of the input contains two integers n and k (2 ≤ n ≤ 200; 0 ≤ k ≤ n) — the length of s and the maximum number of moves you can make. The second line of the input contains the string s consisting of n lowercase Latin letters. The third line of the input contains the string t consisting of two lowercase Latin letters.

Output

Print one integer — the maximum possible number of occurrences of t in s as a subsequence if you replace no more than k characters in s optimally.

Examples

Input


4 2
bbaa
ab


Output


3


Input


7 3
asddsaf
sd


Output


10


Input


15 6
qwertyhgfdsazxc
qa


Output


16


Input


7 2
abacaba
aa


Output


15

Note

In the first example, you can obtain the string "abab" replacing s_1 with 'a' and s_4 with 'b'. Then the answer is 3.

In the second example, you can obtain the string "ssddsdd" and get the answer 10.

In the fourth example, you can obtain the string "aaacaaa" and get the answer 15.

Solution (in JAVA):

Solution:
// Don't place your source in a package
import java.util.*;
import java.lang.*;
import java.io.*;
import java.math.*; 
// Please name your class Main
public class Main {
	
	static StreamTokenizer in = new StreamTokenizer(new BufferedReader(new InputStreamReader(System.in)));
    
 
    static int read() throws IOException {
        in.nextToken();
        return (int) in.nval;
    }
    static String readString() throws IOException {
        in.nextToken();
        return in.sval;
	}
	
	
	public static void main (String[] args) throws java.lang.Exception {
	    Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		//InputReader in = new InputReader(System.in);
		
		
		int n=in.nextInt();
		int k=in.nextInt();
		
		String s1=in.next();
		String s2=in.next();
		
		Solution sol=new Solution();
		sol.solution(n,k,s1,s2);
		
		
		out.flush();	
		
		
		

		
		}
 
}
 
class Solution{
	//constant variable
	final int MAX=Integer.MAX_VALUE;
	final int MIN=Integer.MIN_VALUE;
	//Set<Integer>adjecent[];
	//////////////////////////////
 

 
	//int dp[][][];
	//Map<String,int[]>map=new HashMap<>();
	char c1,c2;
	int dp[][][];
	public void solution(int n,int k, String s1,String s2){
		//s2 only has len2
		
		if(s2.charAt(0)==s2.charAt(1)){
			int cnt=0;
			for(int i=0;i<s1.length();i++){
				if(s1.charAt(i)==s2.charAt(0))cnt++;
			}
			cnt=Math.min(s1.length(),cnt+k);
			cnt--;
			cnt=cnt*(1+cnt)/2;
			msg(cnt+"");
			return;
		}
		
		c1=s2.charAt(0);
		c2=s2.charAt(1);
		dp=new int[s1.length()+1][s1.length()+1][s1.length()+1];
		for(int i=0;i<dp.length;i++){
			for(int j=0;j<dp[0].length;j++){
				Arrays.fill(dp[i][j],-1);
			}
		}
		
		int res = dfs(s1,0,k,0);
		
		/*for(int i=0;i<dp.length;i++){
			for(int j=0;j<dp[0].length;j++){
				print1(dp[i][j]);
			}
		}*/
		
		msg(res+"");
	}
	
	public int dfs(String s1,int i,int k,int pre){
		if(i>=s1.length())return 0;
		if(dp[i][k][pre]!=-1)return dp[i][k][pre];
		char c=s1.charAt(i);
		int res=0;
		if(c==c1){
			res=Math.max(res,dfs(s1,i+1,k,pre+1));
			if(k>0){
				res=Math.max(res,pre+dfs(s1,i+1,k-1,pre));
			}
		}
		else if(c==c2){
			if(k>0){
				res=Math.max(res,dfs(s1,i+1,k-1,pre+1));
			}
			res=Math.max(res,pre+dfs(s1,i+1,k,pre));
		}else{
			res=Math.max(res,dfs(s1,i+1,k,pre));
			if(k>0){
				res=Math.max(res,pre+dfs(s1,i+1,k-1,pre));
				res=Math.max(res,dfs(s1,i+1,k-1,pre+1));
			}
		}
		
		//msg(i+"  "+k+"  "+pre);
		
		dp[i][k][pre]=res;
		return res;
	}
	
	
 
	
	
	
 
	
	
	
 
 
	/*public void tarjan(int p,int r){
		if(cut)return;
		List<Integer>childs=adjecent[r];
		dis[r]=low[r]=time;
		time++;
		
		//core for tarjan
		int son=0;
		for(int c:childs){
			if(ban==c||c==p)continue;
			if(dis[c]==-1){
				son++;
				tarjan(r,c);
				low[r]=Math.min(low[r],low[c]);
				if((r==root&&son>1)||(low[c]>=dis[r]&&r!=root)){
					cut=true;
					return;
				}
			}else{
				if(c!=p){
					low[r]=Math.min(low[r],dis[c]);
				}
			}
		}
		
	}*/
	
	
 
	
	
		
	
	//helper function I would use
	public void ascii(String s){
		for(char c:s.toCharArray()){
			System.out.print((c-'a')+" ");
		}
		msg("");
	}
	
	public int flip(int i){
		if(i==0)return 1;
		else return 0;
	}
	
	public boolean[] primes(int n){
		boolean A[]=new boolean[n+1];
		for(int i=2;i<=n;i++){
			if(A[i]==false){
				for(int j=i+i;j<=n;j+=i){
					A[j]=true;
				}
			}
		}
		return A;
	}
	
	public void msg(String s){
		System.out.println(s);
	}
	
	public int[] kmpPre(String p){
		int pre[]=new int[p.length()];
		int l=0,r=1;
		while(r<p.length()){
			if(p.charAt(l)==p.charAt(r)){
				pre[r]=l+1;
				l++;r++;
			}else{
				if(l==0)r++;
				else l=pre[l-1];
			}
		}
		return pre;
	}
	
	public boolean isP(String s){
		int l=0,r=s.length()-1;
		while(l<r){
			if(s.charAt(l)!=s.charAt(r))return false;
			l++;r--;
		}
		return true;
	}
	
	public int find(int nums[],int x){//union find => find method
		if(nums[x]==x)return x;
		int root=find(nums,nums[x]);
		nums[x]=root;
		return root;
	}
	
	public boolean check(int grid[][],int r,int c){
		if(r<0||c<0||r>=grid.length||c>=grid[0].length)return false;
		return true;
	}
	
	public int get(int A[],int i){
		if(i<0||i>=A.length)return 0;
		return A[i];
	}
	public int[] copy1(int A[]){
		int a[]=new int[A.length];
		for(int i=0;i<a.length;i++)a[i]=A[i];
		return a;
	}
	
	public int[] copy2(int A[]){
		int a[]=new int[A.length];
		for(int i=0;i<a.length;i++)a[i]=A[i];
		return a;
	}
	
	
	public void print1(int A[]){
		for(long i:A)System.out.print(i+" ");
		System.out.println();
	}
	public void print2(int A[][]){
		for(int i=0;i<A.length;i++){
			for(int j=0;j<A[0].length;j++){
				System.out.print(A[i][j]+" ");
			}System.out.println();
		}
	}
	
	public int min(int a,int b){
		return Math.min(a,b);
	}
	
	
	public int[][] matrixdp(int[][] grid) {
        if(grid.length==0)return new int[][]{};
        int res[][]=new int[grid.length][grid[0].length];
        for(int i=0;i<grid.length;i++){
            for(int j=0;j<grid[0].length;j++){
                res[i][j]=grid[i][j]+get(res,i-1,j)+get(res,i,j-1)-get(res,i-1,j-1);
            }
        }
        return res;
    }
    
    public int get(int grid[][],int i,int j){
        if(i<0||j<0||i>=grid.length||j>=grid[0].length)return 0;
        return grid[i][j];
    }
	
	public int[] suffixArray(String s){
		int n=s.length();
		Suffix A[]=new Suffix[n];
		
		for(int i=0;i<n;i++){
			A[i]=new Suffix(i,s.charAt(i)-'a',0);
		}
		
		for(int i=0;i<n;i++){
			if(i==n-1){
				A[i].next=-1;
			}else{
				A[i].next=A[i+1].rank;
			}
		}
		Arrays.sort(A);
		
		for(int len=4;len<A.length*2;len<<=1){
			int in[]=new int[A.length];
			int rank=0;
			int pre=A[0].rank;
			A[0].rank=rank;
			in[A[0].index]=0;
			for(int i=1;i<A.length;i++){//rank for the first two letter
				if(A[i].rank==pre&&A[i].next==A[i-1].next){
					pre=A[i].rank;
					A[i].rank=rank;
				}else{
					pre=A[i].rank;
					A[i].rank=++rank;
				}
				in[A[i].index]=i;
			}
			
			for(int i=0;i<A.length;i++){
				int next=A[i].index+len/2;
				if(next>=A.length){
					A[i].next=-1;
				}else{
					A[i].next=A[in[next]].rank;
				}
			}
			
			
			Arrays.sort(A);
		}
		
		
		int su[]=new int[A.length];
		for(int i=0;i<su.length;i++){
			su[i]=A[i].index;
		}
		return su;
	}
	
}

//suffix array Struct
class Suffix implements Comparable<Suffix>{
	int index;
	int rank;
	int next;
	public Suffix(int i,int rank,int next){
		this.index=i;
		this.rank=rank;
		this.next=next;
	}
	
	@Override
	public int compareTo(Suffix other) {
		if(this.rank==other.rank){
			return this.next-other.next;
		}
		return this.rank-other.rank;
	}
	
	public String toString(){
		return this.index+"   "+this.rank+"   "+this.next+"  ";
	}
}




 
class Wrapper implements Comparable<Wrapper>{
	int spf;int cnt;
	public Wrapper(int spf,int cnt){
		this.spf=spf;
		this.cnt=cnt;
	}
		
	@Override
	public int compareTo(Wrapper other) {
		return this.spf-other.spf;
	}
}