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
/*
    Author: Anthony Ngene
    Created: 02/09/2020 - 07:58
*/

import java.io.*;
import java.util.*;

public class D2 {
// Being deeply loved by someone gives you strength, while loving someone deeply gives you courage. - Lao Tzu
    public static void main(String[] args) throws IOException {
        in = new FastScanner();

        String lng = in.next();
        String sht = in.next();
        int n = lng.length();
        int m = sht.length();
        int[] leftmost = new int[m + 1];
        int[] rightmost = new int[m + 1];
        rightmost[m] = n;

        int idx = 0;
        for (int i = 0; i < m; i++) {
            while (sht.charAt(i) != lng.charAt(idx)) idx++;
            leftmost[i] = idx;
            idx++;
        }
        idx = n - 1;
        for (int i = m - 1; i >= 0; i--) {
            while (sht.charAt(i) != lng.charAt(idx)) idx--;
            rightmost[i] = idx;
            idx--;
        }
;
        int ans = rightmost[0];
        for (int i = 0; i < m; i++)
            ans = max(ans, rightmost[i + 1] - leftmost[i] - 1);
        out.println(ans);

        out.close();
    }


// checks: 1. edge cases   2. overflow   3. possible errors (e.g 1/0, arr[out])   4. time/space complexity
// Generated Code Below:
private static final FastWriter out = new FastWriter();
private static FastScanner in;
static ArrayList<Integer>[] adj;
private static long e97 = (long)1e9 + 7;
static class FastWriter {
    private static final int IO_BUFFERS = 128 * 1024;
    private final StringBuilder out;
    public FastWriter() { out = new StringBuilder(IO_BUFFERS); }
    public FastWriter p(Object object) { out.append(object); return this; }
    public FastWriter p(String format, Object... args) { out.append(String.format(format, args)); return this; }
    public FastWriter pp(Object... args) { for (Object ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public FastWriter pp(int[] args) { for (int ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public FastWriter pp(long[] args) { for (long ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public FastWriter pp(char[] args) { for (char ob : args) { out.append(ob).append(" ");  } out.append("\n"); return this; }
    public void println(long[] arr) { for(long e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(int[] arr) { for(int e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(char[] arr) { for(char e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(double[] arr) { for(double e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(boolean[] arr) { for(boolean e: arr) out.append(e).append(" "); out.append("\n"); }
    public <T>void println(T[] arr) { for(T e: arr) out.append(e).append(" "); out.append("\n"); }
    public void println(long[][] arr) {  for (long[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(int[][] arr) {  for (int[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(char[][] arr) {  for (char[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public void println(double[][] arr) {  for (double[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public <T>void println(T[][] arr) {  for (T[] row: arr) out.append(Arrays.toString(row)).append("\n"); }
    public FastWriter println(Object object) { out.append(object).append("\n"); return this; }
    public void toFile(String fileName) throws IOException {
        BufferedWriter writer = new BufferedWriter(new FileWriter(fileName));
        writer.write(out.toString());
        writer.close();
    }
    public void close() throws IOException { System.out.print(out); }
}
static class FastScanner {
    private InputStream sin = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    public FastScanner(){}
    public FastScanner(String filename) throws FileNotFoundException {
        File file = new File(filename);
        sin = new FileInputStream(file);
    }
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        }else{
            ptr = 0;
            try {
                buflen = sin.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }
    private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
    private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
    public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while(isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    public long longNext() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while(true){
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            }else if(b == -1 || !isPrintableChar(b) || b == ':'){
                return minus ? -n : n;
            }else{
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }
    public int intNext() {
        long nl = longNext();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
        return (int) nl;
    }
    public double doubleNext() { return Double.parseDouble(next());}
    public long[] nextLongArray(final int n){
        final long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = longNext();
        return a;
    }
    public int[] nextIntArray(final int n){
        final int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = intNext();
        return a;
    }
    public double[] nextDoubleArray(final int n){
        final double[] a = new double[n];
        for (int i = 0; i < n; i++)
            a[i] = doubleNext();
        return a;
    }
    public ArrayList<Integer>[] getAdj(int n) {
        ArrayList<Integer>[] adj = new ArrayList[n + 1];
        for (int i = 1; i <= n; i++) adj[i] = new ArrayList<>();
        return adj;
    }
    public ArrayList<Integer>[] adjacencyList(int nodes, int edges) throws IOException {
        return adjacencyList(nodes, edges, false);
    }
    public ArrayList<Integer>[] adjacencyList(int nodes, int edges, boolean isDirected) throws IOException {
        adj = getAdj(nodes);
        for (int i = 0; i < edges; i++) {
            int a = intNext(), b = intNext();
            adj[a].add(b);
            if (!isDirected) adj[b].add(a);
        }
        return adj;
    }
}
static class u {
    public static int upperBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj < array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    public static int upperBound(ArrayList<Long> array, long obj) {
        int l = 0, r = array.size() - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj < array.get(c)) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    public static int lowerBound(long[] array, long obj) {
        int l = 0, r = array.length - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj <= array[c]) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    public static int lowerBound(ArrayList<Long> array, long obj) {
        int l = 0, r = array.size() - 1;
        while (r - l >= 0) {
            int c = (l + r) / 2;
            if (obj <= array.get(c)) {
                r = c - 1;
            } else {
                l = c + 1;
            }
        }
        return l;
    }
    static <T> T[][] deepCopy(T[][] matrix) { return Arrays.stream(matrix).map(el -> el.clone()).toArray($ -> matrix.clone()); }
    static int[][] deepCopy(int[][] matrix) { return Arrays.stream(matrix).map(int[]::clone).toArray($ -> matrix.clone()); }
    static long[][] deepCopy(long[][] matrix) { return Arrays.stream(matrix).map(long[]::clone).toArray($ -> matrix.clone()); }
    private static void sort(int[][] arr){ Arrays.sort(arr, Comparator.comparingDouble(o -> o[0])); }
    private static void sort(long[][] arr){ Arrays.sort(arr, Comparator.comparingDouble(o -> o[0])); }
    private static <T>void rSort(T[] arr) { Arrays.sort(arr, Collections.reverseOrder()); }
    private static void customSort(int[][] arr) {
        Arrays.sort(arr, new Comparator<int[]>() {
            public int compare(int[] a, int[] b) {
                if (a[0] == b[0]) return Integer.compare(a[1], b[1]);
                return Integer.compare(a[0], b[0]);
            }
        });
    }
    public static int[] swap(int[] arr, int left, int right) {
        int temp = arr[left];
        arr[left] = arr[right];
        arr[right] = temp;
        return arr;
    }
    public static int[] reverse(int[] arr, int left, int right) {
        while (left < right) {
            int temp = arr[left];
            arr[left++] = arr[right];
            arr[right--] = temp;
        }
        return arr;
    }
    public static boolean findNextPermutation(int[] data) {
        if (data.length <= 1) return false;
        int last = data.length - 2;
        while (last >= 0) {
            if (data[last] < data[last + 1]) break;
            last--;
        }
        if (last < 0) return false;
        int nextGreater = data.length - 1;
        for (int i = data.length - 1; i > last; i--) {
            if (data[i] > data[last]) {
                nextGreater = i;
                break;
            }
        }
        data = swap(data, nextGreater, last);
        data = reverse(data, last + 1, data.length - 1);
        return true;
    }
    public static int biSearch(int[] dt, int target){
        int left=0, right=dt.length-1;
        int mid=-1;
        while(left<=right){
            mid = (right+left)/2;
            if(dt[mid] == target) return mid;
            if(dt[mid] < target) left=mid+1;
            else right=mid-1;
        }
        return -1;
    }
    public static int biSearchMax(long[] dt, long target){
        int left=-1, right=dt.length;
        int mid=-1;

        while((right-left)>1){
            mid = left + (right-left)/2;
            if(dt[mid] <= target) left=mid;
            else right=mid;
        }
        return left;
    }
    public static int biSearchMaxAL(ArrayList<Integer> dt, long target){
        int left=-1, right=dt.size();
        int mid=-1;

        while((right-left)>1){
            mid = left + (right-left)/2;
            if(dt.get(mid) <= target) left=mid;
            else right=mid;
        }
        return left;
    }
    private static <T>void fill(T[][] ob, T res){for(int i=0;i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(boolean[][] ob,boolean res){for(int i=0;i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(int[][] ob, int res){      for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(long[][] ob, long res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(char[][] ob, char res){    for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(double[][] ob, double res){for(int i=0; i<ob.length; i++){ for(int j=0; j<ob[0].length; j++){  ob[i][j] = res; }}}
    private static void fill(int[][][] ob,int res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
    private static void fill(long[][][] ob,long res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
    private static <T>void fill(T[][][] ob,T res){for(int i=0;i<ob.length;i++){for(int j=0;j<ob[0].length;j++){for(int k=0;k<ob[0][0].length;k++){ob[i][j][k]=res;}}}}
    private static void fill_parent(int[] ob){ for(int i=0; i<ob.length; i++) ob[i]=i; }
    private static boolean same3(long a, long b, long c){
        if(a!=b) return false;
        if(b!=c) return false;
        if(c!=a) return false;
        return true;
    }
    private static boolean dif3(long a, long b, long c){
        if(a==b) return false;
        if(b==c) return false;
        if(c==a) return false;
        return true;
    }
    private static double hypotenuse(double a, double b){
        return Math.sqrt(a*a+b*b);
    }
    private static long factorial(int n) {
        long ans=1;
        for(long i=n; i>0; i--){ ans*=i; }
        return ans;
    }
    private static long facMod(int n, long mod) {
        long ans=1;
        for(long i=n; i>0; i--) ans = (ans * i) % mod;
        return ans;
    }
    private static long lcm(long m, long n){
        long ans = m/gcd(m,n);
        ans *= n;
        return ans;
    }
    private static long gcd(long m, long n) {
        if(m < n) return gcd(n, m);
        if(n == 0) return m;
        return gcd(n, m % n);
    }
    private static boolean isPrime(long a){
        if(a==1) return false;
        for(int i=2; i<=Math.sqrt(a); i++){  if(a%i == 0) return false;  }
        return true;
    }
    static long modInverse(long a, long mod) {
    /* Fermat's little theorem: a^(MOD-1) => 1
    Therefore (divide both sides by a): a^(MOD-2) => a^(-1) */
        return binpowMod(a, mod - 2, mod);
    }
    static long binpowMod(long a, long b, long mod) {
        long res = 1;
        while (b > 0) {
            if (b % 2 == 1) res = (res * a) % mod;
            a = (a * a) % mod;
            b /= 2;
        }
        return res;
    }
    private static int getDigit2(long num){
        long cf = 1;    int d=0;
        while(num >= cf){   d++;    cf = 1<<d;  }
        return d;
    }
    private static int getDigit10(long num){
        long cf = 1;    int d=0;
        while(num >= cf){   d++;    cf*=10;     }
        return d;
    }
    private static boolean isInArea(int y, int x, int h, int w){
        if(y<0) return false;
        if(x<0) return false;
        if(y>=h) return false;
        if(x>=w) return false;
        return true;
    }
    private static ArrayList<Integer> generatePrimes(int n) {
        int[] lp = new int[n + 1];
        ArrayList<Integer> pr = new ArrayList<>();
        for (int i = 2; i <= n; ++i) {
            if (lp[i] == 0) {
                lp[i] = i;
                pr.add(i);
            }
            for (int j = 0; j < pr.size() && pr.get(j) <= lp[i] && i * pr.get(j) <= n; ++j) {
                lp[i * pr.get(j)] = pr.get(j);
            }
        }
        return pr;
    }
    static long nPrMod(int n, int r, long MOD) {
        long res = 1;
        for (int i = (n - r + 1); i <= n; i++) {
            res = (res * i) % MOD;
        }
        return res;
    }
    static long nCr(int n, int r) {
        if (r > (n - r))
            r = n - r;
        long ans = 1;
        for (int i = 1; i <= r; i++) {
            ans *= n;
            ans /= i;
            n--;
        }
        return ans;
    }
    static long nCrMod(int n, int r, long MOD) {
        long rFactorial = nPrMod(r, r, MOD);
        long first = nPrMod(n, r, MOD);
        long second = binpowMod(rFactorial, MOD-2, MOD);
        return  (first * second) % MOD;
    }
    static void printBitRepr(int n) {
        StringBuilder res = new StringBuilder();
        for (int i = 0; i < 32; i++) {
            int mask = (1 << i);
            res.append((mask & n) == 0 ? "0" : "1");
        }
        out.println(res);
    }
    static String bitString(int n) {return Integer.toString(n);}
    static int setKthBitToOne(int n, int k) { return (n | (1 << k)); } // zero indexed
    static int setKthBitToZero(int n, int k) { return (n & ~(1 << k)); }
    static int invertKthBit(int n, int k) { return (n ^ (1 << k)); }
    static boolean isPowerOfTwo(int n) { return (n & (n - 1)) == 0; }
    static HashMap<Character, Integer> counts(String word) {
        HashMap<Character, Integer> counts = new HashMap<>();
        for (int i = 0; i < word.length(); i++) counts.merge(word.charAt(i), 1, Integer::sum);
        return counts;
    }
    static HashMap<Integer, Integer> counts(int[] arr) {
        HashMap<Integer, Integer> counts = new HashMap<>();
        for (int value : arr) counts.merge(value, 1, Integer::sum);
        return counts;
    }
    static HashMap<Long, Integer> counts(long[] arr) {
        HashMap<Long, Integer> counts = new HashMap<>();
        for (long l : arr) counts.merge(l, 1, Integer::sum);
        return counts;
    }
    static HashMap<Character, Integer> counts(char[] arr) {
        HashMap<Character, Integer> counts = new HashMap<>();
        for (char c : arr) counts.merge(c, 1, Integer::sum);
        return counts;
    }
    static long hash(int x, int y) {
        return x* 1_000_000_000L +y;
    }
}
static class Tuple implements Comparable<Tuple> {
    long a;
    long b;
    long c;
    public Tuple(long a, long b) {
        this.a = a;
        this.b = b;
        this.c = 0;
    }
    public Tuple(long a, long b, long c) {
        this.a = a;
        this.b = b;
        this.c = c;
    }
    public long getA() { return a; }
    public long getB() { return b; }
    public long getC() { return c; }
    public int compareTo(Tuple other) {
        if (this.a == other.a) {
            if (this.b == other.b) return Long.compare(this.c, other.c);
            return Long.compare(this.b, other.b);
        }
        return Long.compare(this.a, other.a);
    }
    @Override
    public int hashCode() { return Arrays.deepHashCode(new Long[]{a, b, c}); }
    @Override
    public boolean equals(Object o) {
        if (!(o instanceof Tuple)) return false;
        Tuple pairo = (Tuple) o;
        return (this.a == pairo.a && this.b == pairo.b && this.c == pairo.c);
    }
    @Override
    public String toString() { return String.format("(%d %d %d)  ", this.a, this.b, this.c); }
}
private static int abs(int a){  return (a>=0) ? a: -a;  }
private static int min(int... ins){ int min = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] < min) min = ins[i]; } return min; }
private static int max(int... ins){ int max = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] > max) max = ins[i]; } return max; }
private static int sum(int... ins){ int total = 0; for (int v : ins) { total += v; } return total; }
private static long abs(long a){    return (a>=0) ? a: -a;  }
private static long min(long... ins){ long min = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] < min) min = ins[i]; } return min; }
private static long max(long... ins){ long max = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] > max) max = ins[i]; } return max; }
private static long sum(long... ins){ long total = 0; for (long v : ins) { total += v; } return total; }
private static double abs(double a){    return (a>=0) ? a: -a;  }
private static double min(double... ins){ double min = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] < min) min = ins[i]; } return min; }
private static double max(double... ins){ double max = ins[0]; for(int i=1; i<ins.length; i++){ if(ins[i] > max) max = ins[i]; } return max; }
private static double sum(double... ins){ double total = 0; for (double v : ins) { total += v; } return total; }

}
