Unable to read a file from a different method

I am a beginner in java and trying to solve the below use case.
Use case : From a file(input.txt) having numbers, find out and write all the unique numbers to a different file(output.txt) without using any Data structures(array, set, map, etc…).
For the mentioned use case I wrote the following code in java:

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

class Merge{
    public static boolean doesExist(String mobileNo) throws IOException{
        BufferedReader reader = new BufferedReader(new FileReader("output.txt"));
        String exist = reader.readLine();
        
        //logging
        System.out.println(exist + " " + mobileNo);
        
        while(exist != null){
            if(exist.equals(mobileNo)) return true;
            exist = reader.readLine();
        }
        return false;
    }
    
    public static void main(String[] args) throws IOException{
        
        PrintWriter writer = new PrintWriter("output.txt");
        BufferedReader reader = new BufferedReader(new FileReader("input.txt"));
        
        
        String mobileNo = reader.readLine();
        
        while(mobileNo != null){
            if(!doesExist(mobileNo)) writer.println(mobileNo);
            mobileNo = reader.readLine();
        }
        
        writer.flush();
        reader.close();
        writer.close();
        
        return ;
    }
}

The above program is not filtering the unique numbers, the output picture is attached.

I tried to debugg using the console printing, and found that the output.txt is not getting read.
The following is the console output of logging:

The input is as follows:

Someone please help me explaining why this is happening.

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