Null pointer exception

Code:

package Obj1_3_1_4;
public class ArrEx
{
    // Arrays are can be declared like this
    int[] a;
    int b[];
    int[][] c;
    int[] d[][];
    String[] S;// Array of string class objects
    public static void main(String[] args)
    {
        int i=0,j=0,k=0;
        ArrEx AE=new ArrEx();
        
        for(i=0;i<10;i++)
        {
            AE.a[i]=6;
            AE.b[i]=44;
        }
        for(i=0;i<10;i++)
        for(j=0;j<10;j++)
        AE.c[i][j]=644;
        
        for(i=0;i<10;i++)
        for(j=0;j<10;j++)
        for(k=0;k<10;k++)
        AE.d[i][j][k]=1;
        
        for(i=0;i<10;i++)
        AE.S[i]="S";
        
        for(i=0;i<10;i++)
        {
            System.out.println(AE.a[i]);
            System.out.println(AE.b[i]);
        }
        
    for(i=0;i<10;i++)
        for(j=0;j<10;j++)
        System.out.println(AE.c[i][j]);
        
        for(i=0;i<10;i++)
        for(j=0;j<10;j++)
        for(k=0;k<10;k++)
        System.out.println(AE.d[i][j][k]);
        
        for(i=0;i<10;i++)
        System.out.println(AE.S[i]);
    }
}

This program compiles fine and...the output while executing is
Exception in thread "main" java.lang.NullPointerException
at Obj1_3_1_4.ArrEx.main(ArrEx.java:20)
Please help...