The only difference between easy and hard versions is the length of the string.

You are given a string s and a string t, both consisting only of lowercase Latin letters. It is guaranteed that t can be obtained from s by removing some (possibly, zero) number of characters (not necessary contiguous) from s without changing order of remaining characters (in other words, it is guaranteed that t is a subsequence of s).

For example, the strings "test", "tst", "tt", "et" and "" are subsequences of the string "test". But the strings "tset", "se", "contest" are not subsequences of the string "test".

You want to remove some substring (contiguous subsequence) from s of maximum possible length such that after removing this substring t will remain a subsequence of s.

If you want to remove the substring s[l;r] then the string s will be transformed to s_1 s_2 ... s_{l-1} s_{r+1} s_{r+2} ... s_{|s|-1} s_{|s|} (where |s| is the length of s).

Your task is to find the maximum possible length of the substring you can remove so that t is still a subsequence of s.

Input

The first line of the input contains one string s consisting of at least 1 and at most 2 ⋅ 10^5 lowercase Latin letters.

The second line of the input contains one string t consisting of at least 1 and at most 2 ⋅ 10^5 lowercase Latin letters.

It is guaranteed that t is a subsequence of s.

Output

Print one integer — the maximum possible length of the substring you can remove so that t is still a subsequence of s.

Examples

Input


bbaba
bb


Output


3


Input


baaba
ab


Output


2


Input


abcde
abcde


Output


0


Input


asdfasdf
fasd


Output


3
import java.util.*;

import java.io.*;
import java.math.*;

/**
 * @author Naitik
 * 
 */

public class A		
{ 
			 static FastReader sc=new FastReader(); 
			 static long dp[][];
			 static int mod=1000000007;
			 static int max;
			 static int bit[];
			 static long ans;
			 static HashMap<Integer,Integer> map;
			
				
		     public static void main(String[] args)
		    {
		    	//CHECK FOR N=1
		        	//CHECK FOR N=1
			  PrintWriter out=new PrintWriter(System.out);
			  StringBuffer sb=new StringBuffer("");
			 
		  int ttt=1;
		    // ttt =i();
		   
		    outer :while (ttt-- > 0) 
			{	
		    	char A[]=s().toCharArray();
		    	char B[]=s().toCharArray();
		    	int n=A.length;
		    	int m=B.length;
		    	int C[]=new int[m];
		    	int D[]=new int[m];
		    	int i=0;
		    	int j=0;
		    	while(i<n && j<m) {
		    		if(A[i]==B[j]) {
		    			C[j]=i;
		    			i++;
		    			j++;
		    		}
		    		else
		    			i++;
		    	}
		    	i=n-1;
		    	j=m-1;
		    	while(i>=0 && j>=0) {
		    		if(A[i]==B[j]) {
		    			D[j]=i;
		    			i--;
		    			j--;
		    		}
		    		else
		    			i--;
		    	}
		    	int max=max(0,max(D[0],n-(C[m-1]+1)));
		    	for(i=0;i<m-1;i++) {
		    		int y=D[i+1]-C[i]-1;
		    		max=max(max,y);
		    	}
		    	System.out.println(max);
		    	
		    	
		    	
		    	
	        	
		    			
		    	
		    	
			}
		   out.close();
		  // System.out.println(sb.toString());
		   
		   
		   //CHECK FOR N=1                    //CHECK FOR M=0
		    //CHECK FOR N=1                    //CHECK FOR M=0
		   
    }

static class Pair implements Comparable<Pair>
     {
    	 int x;
    	 int y;
    	 Pair(int x,int y){
    		 this.x=x;
    		 this.y=y;
    		 
    	 }
		@Override
		public int compareTo(Pair o) {
			int a=o.y-o.x;
			int b=this.y-this.x;
			if(a>b)
				return 1;
			else if(a<b)
				return -1;
			else {
				
					return 0;
			}
		}
		
		/* FOR TREE MAP PAIR USE */
		
//		public int compareTo(Pair o) {
// 			if (x > o.x) {
// 				return 1;
// 			}
// 			if (x < o.x) {
// 				return -1;
// 			}
// 			if (y > o.y) {
// 				return 1;
// 			}
// 			if (y < o.y) {
// 				return -1;
// 			}
// 			return 0;
// 		}
//		public int hashCode() 
//		{ 
//			final int temp = 14; 
//			int ans = 1; 
//			ans =x*31+y*13; 
//			return ans; 
//		} 
//  
//		// Equal objects must produce the same 
//		// hash code as long as they are equal 
//		@Override
//		public boolean equals(Object o) 
//		{ 
//			if (this == o) { 
//				return true; 
//			} 
//			if (o == null) { 
//				return false; 
//			} 
//			if (this.getClass() != o.getClass()) { 
//				return false; 
//			} 
//			Pair other = (Pair)o; 
//			if (this.x != other.x || this.y!=other.y) { 
//				return false; 
//			} 
//			return true; 
//		} 	
		
     }
//FRENWICK TREE
static void update(int i, int x){
	for(; i < bit.length; i += (i&-i))
		bit[i] += x;
}

static int sum(int i){
	int ans = 0;
	for(; i > 0; i -= (i&-i))
		ans += bit[i];
	return ans;
}
//END
static void add(int v) {
	if(!map.containsKey(v)) {
		map.put(v, 1);
	}
	else {
		map.put(v, map.get(v)+1);
	}
}
static void remove(int v) {
	if(map.containsKey(v)) {
		map.put(v, map.get(v)-1);
		if(map.get(v)==0)
			map.remove(v);
	}
}
static int[] copy(int A[]) {
	int B[]=new int[A.length];
	for(int i=0;i<A.length;i++) {
		B[i]=A[i];
	}
	return B;
}
static long[] copy(long A[]) {
	long B[]=new long[A.length];
	for(int i=0;i<A.length;i++) {
		B[i]=A[i];
	}
	return B;
}
static int[] input(int n) {
	int A[]=new int[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextInt();
	   }
	   return A;
   }
static long[] inputL(int n) {
	long A[]=new long[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.nextLong();
	   }
	   return A;
   }
static String[] inputS(int n) {
	String A[]=new String[n];
	   for(int i=0;i<n;i++) {
		   A[i]=sc.next();
	   }
	   return A;
   }
static long sum(int A[]) {
	long sum=0;
	for(int i : A) {
		sum+=i;
	}
	return sum;
}
static long sum(long A[]) {
	long sum=0;
	for(long i : A) {
		sum+=i;
	}
	return sum;
}
static void reverse(long A[]) {
	int n=A.length;
	long B[]=new long[n];
	for(int i=0;i<n;i++) {
		B[i]=A[n-i-1];
	}
	for(int i=0;i<n;i++)
		A[i]=B[i];
	
}
static void reverse(int A[]) {
	int n=A.length;
	int B[]=new int[n];
	for(int i=0;i<n;i++) {
		B[i]=A[n-i-1];
	}
	for(int i=0;i<n;i++)
		A[i]=B[i];
	
}
static void input(int A[],int B[]) {
	   for(int i=0;i<A.length;i++) {
		   A[i]=sc.nextInt();
		   B[i]=sc.nextInt();
	   }
}
static int[][] input(int n,int m){
	int A[][]=new int[n][m];
	for(int i=0;i<n;i++) {
		for(int j=0;j<m;j++) {
			A[i][j]=i();
		}
	}
	return A;
}
static char[][] charinput(int n,int m){
	char A[][]=new char[n][m];
	for(int i=0;i<n;i++) {
		String s=s();
		for(int j=0;j<m;j++) {
			A[i][j]=s.charAt(j);
		}
	}
	return A;
}
static int find(int A[],int a) {
	  if(A[a]==a)
		  return a;
	  return A[a]=find(A, A[a]);
}
static int max(int A[]) {
	int max=Integer.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static int min(int A[]) {
	int min=Integer.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long max(long A[]) {
	long max=Long.MIN_VALUE;
	for(int i=0;i<A.length;i++) {
		max=Math.max(max, A[i]);
	}
	return max;
}
static long min(long A[]) {
	long min=Long.MAX_VALUE;
	for(int i=0;i<A.length;i++) {
		min=Math.min(min, A[i]);
	}
	return min;
}
static long [] prefix(long A[]) {
	long p[]=new long[A.length];
	p[0]=A[0];
	for(int i=1;i<A.length;i++)
		p[i]=p[i-1]+A[i];
	return p;
}
static long [] prefix(int A[]) {
	long p[]=new long[A.length];
	p[0]=A[0];
	for(int i=1;i<A.length;i++)
		p[i]=p[i-1]+A[i];
	return p;
}
static long [] suffix(long A[]) {
	long p[]=new long[A.length];
	p[A.length-1]=A[A.length-1];
	for(int i=A.length-2;i>=0;i--)
		p[i]=p[i+1]+A[i];
	return p;
}
static long [] suffix(int A[]) {
	long p[]=new long[A.length];
	p[A.length-1]=A[A.length-1];
	for(int i=A.length-2;i>=0;i--)
		p[i]=p[i+1]+A[i];
	return p;
}
static void fill(int dp[]) {
	Arrays.fill(dp, -1);
}
static void fill(int dp[][]) {
	for(int i=0;i<dp.length;i++)
	Arrays.fill(dp[i], -1);
}
static void fill(int dp[][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			Arrays.fill(dp[i][j],-1);
		}
	}
}
static void fill(int dp[][][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			for(int k=0;k<dp[0][0].length;k++) {
			Arrays.fill(dp[i][j][k],-1);
			}
		}
	}
}
static void fill(long dp[]) {
	Arrays.fill(dp, -1);
}
static void fill(long dp[][]) {
	for(int i=0;i<dp.length;i++)
	Arrays.fill(dp[i], -1);
}
static void fill(long dp[][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			Arrays.fill(dp[i][j],-1);
		}
	}
}
static void fill(long dp[][][][]) {
	for(int i=0;i<dp.length;i++) {
		for(int j=0;j<dp[0].length;j++) {
			for(int k=0;k<dp[0][0].length;k++) {
			Arrays.fill(dp[i][j][k],-1);
			}
		}
	}
}
static int min(int a,int b) {
	return Math.min(a, b);
}
static int min(int a,int b,int c) {
	return Math.min(a, Math.min(b, c));
}
static int min(int a,int b,int c,int d) {
	return Math.min(a, Math.min(b, Math.min(c, d)));
}
static int max(int a,int b) {
	return Math.max(a, b);
}
static int max(int a,int b,int c) {
	return Math.max(a, Math.max(b, c));
}
static int max(int a,int b,int c,int d) {
	return Math.max(a, Math.max(b, Math.max(c, d)));
}
static long min(long a,long b) {
	return Math.min(a, b);
}
static long min(long a,long b,long c) {
	return Math.min(a, Math.min(b, c));
}
static long min(long a,long b,long c,long d) {
	return Math.min(a, Math.min(b, Math.min(c, d)));
}
static long max(long a,long b) {
	return Math.max(a, b);
}
static long max(long a,long b,long c) {
	return Math.max(a, Math.max(b, c));
}
static long max(long a,long b,long c,long d) {
	return Math.max(a, Math.max(b, Math.max(c, d)));
}

static long power(long x, long y, long p)
{

	if(y==0)
		return 1;
	if(x==0)
		return 0;
    long res = 1;
    x = x % p;

    while (y > 0) {

        if (y % 2 == 1)
            res = (res * x) % p;

        y = y >> 1; 
        x = (x * x) % p;
    }

    return res;
}
static void print(int A[]) {
	for(int i : A) {
		System.out.print(i+" ");
	}
	System.out.println();
}
static void print(long A[]) {
	for(long i : A) {
		System.out.print(i+" ");
	}
	System.out.println();
}
static long mod(long x) {
	  return ((x%mod + mod)%mod);
}
static String reverse(String s) {
	StringBuffer p=new StringBuffer(s);
	p.reverse();
	return p.toString();
}

     static int i() {
    	 return sc.nextInt();
     }
     static String s() {
    	 return sc.next();
     }
     static long l() {
    	 return sc.nextLong();
     }  
     static void sort(int[] A){
        int n = A.length;
        Random rnd = new Random();
        for(int i=0; i<n; ++i){
            int tmp = A[i];
            int randomPos = i + rnd.nextInt(n-i);
            A[i] = A[randomPos];
            A[randomPos] = tmp;
        }
        Arrays.sort(A);
     }
     static void sort(long[] A){
	        int n = A.length;
	        Random rnd = new Random();
	        for(int i=0; i<n; ++i){
	            long tmp = A[i];
	            int randomPos = i + rnd.nextInt(n-i);
	            A[i] = A[randomPos];
	            A[randomPos] = tmp;
	        }
	        Arrays.sort(A);
	     }
  static String sort(String s) {
 	 Character ch[]=new Character[s.length()];
 	 for(int i=0;i<s.length();i++) {
 		 ch[i]=s.charAt(i);
 	 }
 	 Arrays.sort(ch);
 	 StringBuffer st=new StringBuffer("");
 	 for(int i=0;i<s.length();i++) {
 		 st.append(ch[i]);
 	 }
 	 return st.toString();
  }
  static HashMap<Integer,Integer> hash(int A[]){
	  HashMap<Integer,Integer> map=new HashMap<Integer, Integer>();
	  for(int i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
  }
  static TreeMap<Integer,Integer> tree(int A[]){
	  TreeMap<Integer,Integer> map=new TreeMap<Integer, Integer>();
	  for(int i : A) {
		  if(map.containsKey(i)) {
			  map.put(i, map.get(i)+1);
		  }
		  else {
			  map.put(i, 1);
		  }
	  }
	  return map;
  }
     static boolean prime(int n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static boolean prime(long n) 
	    { 
	        if (n <= 1) 
	            return false; 
	        if (n <= 3) 
	            return true; 
	        if (n % 2 == 0 || n % 3 == 0) 
	            return false; 
	        double sq=Math.sqrt(n);
	  
	        for (int i = 5; i <= sq; i = i + 6) 
	            if (n % i == 0 || n % (i + 2) == 0) 
	                return false; 
	        return true; 
	    } 
     static int gcd(int a, int b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     static long gcd(long a, long b) 
     { 
         if (a == 0) 
             return b; 
         return gcd(b % a, a); 
     } 
     
        
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    } 
} 
