Copying HashMap to another HashMap

I am having a problem copying a HashMap A to HashMap B. B is always same as A. My idea is making a small tile game using HashMaps only.

Map<Point,Tile> A = new HashMap<Point,Tile>();

HashMap has 2 things. A point(key) and a tile object, which is another class I have made. Tile takes in two integers and a string. ( new Tile(x,y,string)). First two integers defines the point x and y and the string tells if its "OFF" or "ON".

What I do first is populate HashMap A with 2*2 elements.

for(int i=0; i<2;i++){
for(int j=0; j<2;j++){
Tile t = new Tile(i, j, "OFF");
A.put(new Point(i,j), t);
}
}

Then I copy HashMap A to HashMap B by adding A in constructor. My idea is so I can go back to default HashMap A by using HashMap B in the constructor(See later)

Map<Point,Tile> B = new HashMap<Point,Tile>(A);

Then I change tile (1,1) to "ON"

Tile t2 = A.get(new Point(1,1));
t2.setS("ON");

One of my tiles is "ON" now. Now I want to reset the board back to original(After the population stage). I clear HashMap A and make a new HashMap with HashMap B as the constructor.

A.clear();
A = new HashMap<Point,Tile>(B);

However, when I changed tile (1,1) to ON on HashMap A , it updated HashMap B as well. I thought making a new HashMap with a constructor will make a new copy of it, but doesn't seem to work.

The strange thing is that

Map<Point,String> A = new HashMap<Point,String>(); 

would work but not

Map<Point,Tile> A = new HashMap<Point,Tile>(); 

I want to somehow get the Original contents of HashMap A without me trying to loop over the elements again.

Here's my main class code

package main;

import java.awt.Point;
import java.util.HashMap;
import java.util.Map;

import model.Tile;

public class Test {

    public static void main(String[] args) {
    //list1
    Map<Point,Tile> A = new HashMap<Point,Tile>();

    //Populating map
    for(int i=0; i<2;i++){
        for(int j=0; j<2;j++){
            Tile t = new Tile(i, j, "OFF");
            A.put(new Point(i,j), t);
        }
    }

    //copying list1 to list2
    Map<Point,Tile> B = new HashMap<Point,Tile>(A);

    //Change tile on 1,1 to ON
    Tile t2 = A.get(new Point(1,1));
    t2.setS("ON");

    for(int i=0; i<2;i++){
        for(int j=0; j<2;j++){
            Tile tTemp = A.get(new Point(i,j));
            System.out.println(i+" "+j+" "+tTemp.getS());
        }
    }

    //Reseting tiles
    //clear first list
    A.clear();
    System.out.println("");
    //copy second list to first list
    A = new HashMap<Point,Tile>(B);


    for(int i=0; i<2;i++){
        for(int j=0; j<2;j++){
            Tile tTemp = A.get(new Point(i,j));
            System.out.println(i+" "+j+" "+tTemp.getS());
            }
        }

    }

}

Here's the tile class

package main;

public class Tile {

public int x,y;
public String s;

public Tile(int x1, int y1, String st){
    x=x1;
    y=y1;
    s=st;
}

public int getX() {
    return x;
}

public void setX(int x) {
    this.x = x;
}

public int getY() {
    return y;
}

public void setY(int y) {
    this.y = y;
}

public String getS() {
    return s;
}

public void setS(String s) {
    this.s = s;
}

}

Here's what is getting printed before clearing HashMap A

0 0 OFF
0 1 OFF
1 0 OFF
1 1 ON

Here's what is getting printed After clearing HashMap A and then copy B to it.

0 0 OFF
0 1 OFF
1 0 OFF
1 1 ON

No difference.