In a strategic computer game "Settlers II" one has to build defense structures to expand and protect the territory. Let's take one of these buildings. At the moment the defense structure accommodates exactly n soldiers. Within this task we can assume that the number of soldiers in the defense structure won't either increase or decrease.

Every soldier has a rank — some natural number from 1 to k. 1 stands for a private and k stands for a general. The higher the rank of the soldier is, the better he fights. Therefore, the player profits from having the soldiers of the highest possible rank.

To increase the ranks of soldiers they need to train. But the soldiers won't train for free, and each training session requires one golden coin. On each training session all the n soldiers are present.

At the end of each training session the soldiers' ranks increase as follows. First all the soldiers are divided into groups with the same rank, so that the least possible number of groups is formed. Then, within each of the groups where the soldiers below the rank k are present, exactly one soldier increases his rank by one.

You know the ranks of all n soldiers at the moment. Determine the number of golden coins that are needed to increase the ranks of all the soldiers to the rank k.

Input

The first line contains two integers n and k (1 ≤ n, k ≤ 100). They represent the number of soldiers and the number of different ranks correspondingly. The second line contains n numbers in the non-decreasing order. The i-th of them, ai, represents the rank of the i-th soldier in the defense building (1 ≤ i ≤ n, 1 ≤ ai ≤ k).

Output

Print a single integer — the number of golden coins needed to raise all the soldiers to the maximal rank.

Examples

Input

4 4
1 2 2 3


Output

4

Input

4 3
1 1 1 1


Output

5

Note

In the first example the ranks will be raised in the following manner:

1 2 2 3 →  2 2 3 4 →  2 3 4 4 →  3 4 4 4 →  4 4 4 4

Thus totals to 4 training sessions that require 4 golden coins.

import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.*;



import java.math.*;
import java.io.*;
import java.text.*;
import java.math.BigInteger;
public class Main {

	static class Interval {
		      int start;
		      int end;
		      Interval() { start = 0; end = 0; }
		      Interval(int s, int e) { start = s; end = e; }
		  }
	static class pair{
		int x;
		int y;
		public pair(int a,int b) {
			this.x=a;
			this.y=b;
		}
	}
	 public static boolean[] sieve(long n)
	    {
	        boolean[] prime = new boolean[(int)n+1];
	        Arrays.fill(prime,true);
	        prime[0] = false;
	        prime[1] = false;
	        long m = (long)Math.sqrt(n);
	        for(int i=2;i<=m;i++)
	        {
	            if(prime[i])
	            {
	                for(int k=i*i;k<=n;k+=i)
	                {
	                    prime[k] = false;
	                }
	            }
	        }
	        return prime;
	    } 
	 
	 //sorting
	
	 
	public static void sort(long arr[], int l, int r)
	    {
	        if (l < r)
	        {
	            // Find the middle point
	            int m = (l+r)/2;
	 
	            // Sort first and second halves
	            sort(arr, l, m);
	            sort(arr , m+1, r);
	 
	            // Merge the sorted halves
	            merge(arr, l, m, r);
	        }
	    }
	 
	 
	public static void merge(long arr[], int l, int m, int r)
	    {
	        // Find sizes of two subarrays to be merged
	        int n1 = m - l + 1;
	        int n2 = r - m;
	 
	        /* Create temp arrays */
	        long L[] = new long[n1];
	        long R[] = new long[n2];
	 
	        //Copy data to temp arrays
	        for (int i=0; i<n1; ++i)
	            L[i] = arr[l + i];
	        for (int j=0; j<n2; ++j)
	            R[j] = arr[m + 1+ j];
	 
	 
	        /* Merge the temp arrays */
	 
	        // Initial indexes of first and second subarrays
	        int i = 0, j = 0;
	 
	        // Initial index of merged subarry array
	        int k = l;
	        while (i < n1 && j < n2)
	        {
	            if (L[i] <= R[j])
	            {
	                arr[k] = L[i];
	                i++;
	            }
	            else
	            {
	                arr[k] = R[j];
	                j++;
	            }
	            k++;
	        }
	 
	        /* Copy remaining elements of L[] if any */
	        while (i < n1)
	        {
	            arr[k] = L[i];
	            i++;
	            k++;
	        }
	 
	        /* Copy remaining elements of R[] if any */
	        while (j < n2)
	        {
	            arr[k] = R[j];
	            j++;
	            k++;
	        }
	    }
	 
	 
	 public static boolean[] primeseive(long n) {
		 boolean prime[]=new boolean[(int)n+1];
		 
		 Arrays.fill(prime, true);
		 
		 prime[0]=false;
		 prime[1]=false;
		 
		 int m=(int) Math.sqrt(n);
		 
		 for(int i=2;i<=m;i++) {
			 if(prime[i]) {
				 
				 for(int k=i*i;k<=n;k+=i) {
					 prime[k]=false;
				 }
			 }
		 }
		 
		 return prime;
	 }
	 
	    
	    static int GCD(int a,int b)
	    {
	        if(b==0)
	        {
	            return a;
	        }
	        return GCD(b,a%b);
	    }
	 
	    
	    
	    static long gcdnik(long a,long b)
	    {
	        if(b==0)
	        {
	            return a;
	        }
	        return gcdnik(b,a%b);
	    }
	    
	    
	    static long CountCoPrimes(long n)
	    {
	        long res = n;
	        for(int i=2;i*i<=n;i++)
	        {
	            if(n%i==0)
	            {
	                while(n%i==0)
	                {
	                    n/=i;
	                }
	                res-=res/i;
	            }
	        }
	        if(n>1)
	        {
	            res-=res/n;
	        }
	        return res;
	    }
	 
	 
	    
	 
	    
	 
	    static boolean prime(int n)
	    {
	        for(int i=2;i*i<=n;i++)
	        {
	            if(i%2==0 ||i%3==0)
	            {
	                return false;
	            }
	        }
	        return true;
	    }
   static String userIdGeneration(String input1,String input2,int input3,int input4) {
	    	if(input1.length()==input2.length()) {
	    		String arr[]=new String[2];
	    		
	    		arr[0]=input1;
	    		arr[1]=input2;
	    		
	    		Arrays.sort(arr);
	    	char c=arr[0].charAt(0);
	    	   String output=c+arr[1];
	    		
	    	   String k=Integer.toString(input3);
	    	
	    	char d=k.charAt(input4-1);
	    	
	    	output+=d;
	    		
	    	char e=k.charAt(k.length()-input4);
	    	output+=e;
	    	String res="";
	    	for(int i=0;i<output.length();i++) {
	    		if(Character.isUpperCase(output.charAt(i))){
	    			res+=Character.toLowerCase(output.charAt(i));
	    		}
	    		else {
	    			res+=Character.toUpperCase(output.charAt(i));
	    		}
	      	}
	    	return res;
	    	}
	    	
	    	
	    	else  {
String arr[]=new String[2];
	    		arr[0]=input1.length()>input2.length()?input2:input1;
	    		arr[1]=input1.length()>input2.length()?input1:input2;
	    		
	    		char c=arr[0].charAt(0);
	    		
	    		String output=c+arr[1];
	    		
	    	String k=Integer.toString(input3);
	    	
	    	char d=k.charAt(input4-1);
	    	
	    	output+=d;
	    		
	    	char e=k.charAt(k.length()-input4);
	    	output+=e;
	    	String res="";
	    	for(int i=0;i<output.length();i++) {
	    		if(Character.isUpperCase(output.charAt(i))){
	    			res+=Character.toLowerCase(output.charAt(i));
	    		}
	    		else {
	    			res+=Character.toUpperCase(output.charAt(i));
	    		}
	    	}
	    return res;
	    	}
	    	
	    }
	static int length(int len) {
		
		if(len==1) {
			return 1;
		}
		else if(len==2) {
			return 3;
		}
		else if(len==3) {
			return 6;
		}
		else if(len==4) {
			return 10;
		}
		return 0;
	}
	
	
public static int LargestFour(int arr[]) {
	Arrays.sort(arr);

	int n=arr.length;
	int count=0;
	int sum=0;
	for(int i=n-1;i>=1;i--) {
		sum+=arr[i];
	
			count++;
			if(count==4) {
				break;
			
		}
		
	}
	
	if(count<4) {
		sum+=arr[0];
	}
	
	return sum;
}
//Nikunj Gupta
public static void insertionSort(int array[]) {  
    int n = array.length;  
    for (int j = 1; j < n; j++) {  
        int key = array[j];  
        int i = j-1;  
        while ( (i > -1) && ( array [i] > key ) ) {  
            array [i+1] = array [i];  
            i--;  
        }  
        array[i+1] = key;  
    }  
} 



  static String solve23(int n) {
int k=0;
while(true) {
	if(n-2020*k<0) {
		return "NO";
	}
	if((n-2020*k)%2021==0) {
		return "YES";
	}
	k++;
}
	  
	
	}
  public static String swapString(String a, int i, int j) {  
      char[] b =a.toCharArray();  
      char ch;  
      ch = b[i];  
      b[i] = b[j];  
      b[j] = ch;  
      return String.valueOf(b);  
  }  
	public static void permutation(String str,int start,int end,ArrayList<String> l,Set<String>set) {
		
		if(start==end-1) {
			set.add(str);
		}
		
		for(int i=start;i<end;i++) {
			str=swapString(str,start,i);
		
		permutation(str,start+1,end,l,set);
		
		swapString(str,start,i);
		
		}
		
		
		
	}


public static boolean solution(int j) {
	String str=Integer.toString(j);
	int zero=0;
	int one=0;
	for(int i=0;i<str.length();i++) {
		if(str.charAt(i)=='7') {
			one++;
		}else if(str.charAt(i)=='4') {
			zero++;
		}
	}
	
	
	if(one==zero) {
		return true;
	}
	
	
return false;
}
	
	
	


public static ArrayList<Interval> insert(ArrayList<Interval> intervals, Interval newInterval) {


ArrayList<Interval>ans=new ArrayList<Interval>();

int min=Math.min(newInterval.start,newInterval.end);
int max=Math.max(newInterval.end,newInterval.start);
int i=0;
boolean flag=false;
boolean place=false;

while(i<intervals.size()){
    int val1=newInterval.start;
    int val2=newInterval.end;
    
    
    if(min<=val1&&max>=val1&&max<=val2){
    Interval p2=	new Interval(min,val2);
    	ans.add(p2);
        
        place=true;
        
    }
    
    else if(min<val1&&max<val1){
        ans.add(new Interval(min,max));
        place=true; 
        ans.add(new Interval(val1,val2));
        i++;
        break;
       
    }
    else if(min>=val1&&max<=val2){
        ans.add(new Interval(val1,val2));
        place=true;
    }
    
    else if(min>val1&&min>val2){
        ans.add(new Interval(val1,val2));
    }
    else if(min>=val1&&max>val2){
        
         min=Math.min(min,val1);
  i++;
  while(i<intervals.size()){
      Interval na=intervals.get(i);
      
      if(max<=na.end&&max>=na.start){
          Interval ni=new Interval(val1,na.end);
      ans.add(ni);
      flag=true;
      place=true;
         // System.out.println("tes");
        break;
      }
      //System.out.println("tes"+"klkl");
      i++;
      
  }
    
        
        
        
    }
    
    
    
}


while(i<intervals.size()){
    Interval df=intervals.get(i);
    Interval g=new Interval(df.start,df.end);
    ans.add(g);
    
    i++;
}
  



    if(place==false){
     Interval ni=new Interval(min,max);
       //  System.out.println("tes");
       ans.add(ni); 
}

return ans;


  }


public static int lower_bound(ArrayList<Long> ar,long k)
{
    int s=0;
    int e=ar.size();
    while (s !=e)
    {
        int mid = s+e>>1;
        if (ar.get(mid) <k)
        {
            s=mid+1;
        }
        else
        {
            e=mid;
        }
    }
    if(s==ar.size())
    {
        return ar.size()-1;
    }
    return s;
}


	
		
		


        
	       
	       
	      
			
	
	
	
	
 


	


 
 
  
    
   
 private static void printsubsequences(String c, String st) {
	// TODO Auto-generated method stub
	
	 
	 if(c.length()==0) {
		 System.out.println(st);
		 return;
	 }
	 
	 
	 printsubsequences(c.substring(1),st+c.charAt(0));
	 printsubsequences(c.substring(1),st);
	 
	 
}

private static boolean compare(HashMap<Character, Integer> smap, HashMap<Character, Integer> pmap) {
		// TODO Auto-generated method stub
	 
	 for(char ch:smap.keySet()) {
		 if(smap.get(ch)!=pmap.get(ch)) {
			 return false;
		 }
	 }
		return true;
	}


private static boolean BinarySearch(int search, int[] val, int n)
 {
		// TODO Auto-generated method stub
		
	 int start=0;
	 int end=val.length-1;
	 while(start<=end) {
		 int mid=(start+end)/2;
		 
		 
		 if(val[mid]==search) {
			 return true;
		 }
		 else if(val[mid]<search) {
			 start=mid+1;
		 }
		 else {
			 end=mid-1;
		 }
		 
	 }
	 return false;
	 }


	
 
// 
// 
// static long findGCD(ArrayList<Long> arr,long start, long n) 
//	    { 
//	        long result = arr.get((int)start); 
//	        for (int i = (int)start+1; i < n; i++) 
//	            result = GCD(arr.get(i), result); 
//	  
//	        return result; 
//	    } 
//	 
	   
	 
	   

	    static long re(long n)
	    {
	        n+=1;
	        while(n%10==0)
	        {
	            n/=10;
	        }
	        return n;
	    }
	   
	   


	    
	 
	 
	 
	 
	 
	 
	    
	 
	    //xor range query
	    static long xor(long n)
	    {
	 
	        if(n%4==0)
	        {
	            return n;
	        }
	        if(n%4==1)
	        {
	            return  1;
	        }
	        if(n%4==2)
	        {
	            return n+1;
	        }
	        return 0;
	    }
	 
	    static long xor(long a,long b)
	    {
	        return xor(b)^xor(a-1);
	    }
	 
	 
	    
	 
	  
	   
	    
	 
	    
	       
	    
	 
	    
	   
	  
	 
	 

	   
	   
	    static void swap(char c,char p)
	    {
	        char t = c;
	        c = p;
	        p = t;
	    }
	 
	    static long max(long n,long m)
	    {
	        return Math.max(n,m);
	    }
	    static long min(long n,long m)
	    {
	        return Math.min(n,m);
	    }
	 
//	    double nd() throws IOException
//	    {
//	        return Double.parseDouble(in.next());
//	    }
//	    int ni() throws IOException
//	    {
//	        return Integer.parseInt(in.next());
//	    }
//	 
//	    long nl() throws IOException
//	    {
//	        return Long.parseLong(in.next());
//	    }
//	 
//	    String si() throws IOException
//	    {
//	        return in.next();
//	    }
//	 
//	 
	  
	   
	    static int abs(int n)
	    {
	        return Math.abs(n);
	    }
	 
	    static class Scanner 
	    {
	        StringTokenizer st;
	        BufferedReader br;
	 
	        public Scanner(InputStream s){  br = new BufferedReader(new InputStreamReader(s));}
	 
	        public String next() throws IOException 
	        {
	            while (st == null || !st.hasMoreTokens()) 
	            {
	                st = new StringTokenizer(br.readLine());
	            }
	            return st.nextToken();
	        }
	 
	        public int nextInt() throws IOException {return Integer.parseInt(next());}
	        
	        public long nextLong() throws IOException {return Long.parseLong(next());}
	 
	        public String nextLine() throws IOException {return br.readLine();}
	 
	        public boolean ready() throws IOException {return br.ready();}
	 
	 
	    }
	 
	    
public static char[] solve(char arr[]) {
	int i=0;
	
	char ans[]=new char[arr.length];
while(i<arr.length-1) {
	
		if(arr[i]=='B'&&arr[i+1]=='G') {
			ans[i]='G';
			ans[i+1]='B';
			i=i+2;
		}else {
			ans[i]=arr[i];
		i++;
		}
		
		
	}

if(i==arr.length-1) {
	ans[i]=arr[i];
}

	
	
	return ans;
	
}
public static void pairsort(ArrayList<pair>l){
	
	l.sort(new Comparator<pair>() {
		public int compare(pair o1,pair o2) {
			if(o1.x>o2.x) {
				return 1;
			}else {
				return -1;
			}
		}
	});

}

public static void main(String[] args) throws IOException{
  Scanner s=new Scanner(System.in);
  
 int n=s.nextInt();
 int tar=s.nextInt();
 int arr[]=new int[n];
 for(int i=0;i<n;i++) {
	 arr[i]=s.nextInt();
 }
 
   Arrays.sort(arr);
 int operations=0;
   while(true) {
	   int count=0;
	 int i=0;
	 while(i<arr.length) {
	   
		   if(arr[i]==tar) {
			   count++;
		   }
		   else {
		
			   while(i<n-1&&arr[i]==arr[i+1]) {
				   i++;
			   }
			   arr[i]++;
			   
		   }
		   
		   
		   i++;
		   
		 
	 }
	 operations++;
		   
	   
	   if(count==arr.length) {
		   break;
	   }
	Arrays.sort(arr);   
   
   }
System.out.println(operations-1);

}

public static long mod(long x){
    //long M=1000000007;
    
	long M=998244353;
	return (int)((x%M+M)%M);
}

static long add(long a,long b){
    return mod(mod(a)+mod(b));
}


public static  long mul(long a,long b){
    return mod(mod(a)*mod(b));
}

static void printAllKLengthRec(char[] set,
        String prefix,
        int n, int k,ArrayList<String>l)
{

// Base case: k is 0,
// print prefix
if (k == 0)
{
//System.out.println(prefix);
l.add(prefix);
	return;
}

// One by one add all characters
// from set and recursively
// call for k equals to k-1
for (int i = 0; i < n; ++i)
{

// Next character of input added
String newPrefix = prefix + set[i];

// k is decreased, because
// we have added a new character
printAllKLengthRec(set, newPrefix,
         n, k - 1,l);
}
}




	 
	 
	 
	class Pair implements Comparable<Pair>
	{
	   int x,y;
	    public Pair(int x,int y)
	    {
	        this.x = x;
	        this.y = y;
	    }
	    public int compareTo(Pair o)
	    {
	        return this.y-o.y;
	    }
	}
	
	}

