Unlucky year in Berland is such a year that its number n can be represented as n = xa + yb, where a and b are non-negative integer numbers. 

For example, if x = 2 and y = 3 then the years 4 and 17 are unlucky (4 = 20 + 31, 17 = 23 + 32 = 24 + 30) and year 18 isn't unlucky as there is no such representation for it.

Such interval of years that there are no unlucky years in it is called The Golden Age.

You should write a program which will find maximum length of The Golden Age which starts no earlier than the year l and ends no later than the year r. If all years in the interval [l, r] are unlucky then the answer is 0.

Input

The first line contains four integer numbers x, y, l and r (2 ≤ x, y ≤ 1018, 1 ≤ l ≤ r ≤ 1018).

Output

Print the maximum length of The Golden Age within the interval [l, r].

If all years in the interval [l, r] are unlucky then print 0.

Examples

Input

2 3 1 10


Output

1


Input

3 5 10 22


Output

8


Input

2 3 3 5


Output

0

Note

In the first example the unlucky years are 2, 3, 4, 5, 7, 9 and 10. So maximum length of The Golden Age is achived in the intervals [1, 1], [6, 6] and [8, 8].

In the second example the longest Golden Age is the interval [15, 22].
import java.util.Scanner;
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;
import static java.lang.Math.*;

public class main implements Runnable{

    static LinkedList <Integer> adj[];
    static int co=0,f=0;

    static void Check2(int n){
        adj=new LinkedList[n+1];
        for(int i=0;i<=n;i++){
            adj[i]=new LinkedList();
        }

    }
    static void add(int i,int j){
        adj[i].add(j);
    }
    public static void main(String[] args) throws Exception {
        new Thread(null, new main(), "Check2", 1<<26).start();// to increse stack size in java
    }
    static long mod=(long)(1e9+7);
    static long le[];
    static int n;
    public void run(){
        /* Enter your code here. Read input from STDIN. Print output to STDOUT. Your class should be named Solution. */
        //Scanner in=new Scanner(System.in);
        InputReader in=new InputReader(System.in);
        PrintWriter w=new PrintWriter(System.out);


        BigInteger x=new BigInteger(in.readString());
        BigInteger y=new BigInteger(in.readString());
        BigInteger l=new BigInteger(in.readString());
        BigInteger r=new BigInteger(in.readString());

        ArrayList<BigInteger> list=new ArrayList<>();

        for(int a=0;a<=64;a++){
            for(int b=0;b<=64;b++){
                BigInteger tmp=x.pow(a).add(y.pow(b));
                if(tmp.compareTo(l)>=0 && r.compareTo(tmp)>=0){
                    list.add(tmp);
                }
            }
        }
        list.add(l.subtract(BigInteger.ONE));
        list.add(r.add(BigInteger.ONE));
        Collections.sort(list);
        long ans=0;

        for(int i=1;i<list.size();i++){
            BigInteger b=list.get(i).subtract(list.get(i-1));
            long tmp=b.longValue()-1;
            ans=max(ans,tmp);
        }
        w.println(ans);







        // rec("",0,0,3);
        w.close();
    }





    static void dfs(int i,int lvl,int v[]){



        v[i]=1;
        //   System.out.println(i);
        le[1]=(long)(le[1])+1l;
        if(lvl+1<=n){
            le[lvl+1]-=1l;
        }
        Iterator <Integer> ne=adj[i].iterator();
        while(ne.hasNext()){
            int k=ne.next();

            if(v[k]==0){
                v[k]=1;
                dfs(k,lvl+1,v);
            }


        }


    }
    static class node{

        int y;
        int val;

        node(int a,int b){

            y=a;
            val=b;

        }


    }
    static  void rec(String s,int a,int b,int n){

        if(b==n){
            System.out.println(s);
            return ;
        }
        String p=s;
        if(a>b){
            s=p+")" ;
            rec(s,a,b+1,n);
        }
        if(a<n){
            s=p+"(";
            rec(s,a+1,b,n);
        }




    }

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

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

        public int read()
        {
            if (numChars==-1)
                throw new InputMismatchException();

            if (curChar >= numChars)
            {
                curChar = 0;
                try
                {
                    numChars = stream.read(buf);
                }
                catch (IOException e)
                {
                    throw new InputMismatchException();
                }

                if(numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public String nextLine()
        {
            BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
        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 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 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 String readString()
        {
            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 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 readString();
        }

        public interface SpaceCharFilter
        {
            public boolean isSpaceChar(int ch);
        }
    }







}