/**
     * Adds the contents of the int arrays x and y. This method allocates
     * a new int array to hold the answer and returns a reference to that
     * array.
     */
     private   static   int [] add( int [] x,  int [] y) {
        // If x is shorter, swap the two arrays
         if  (x.length < y.length) {
             int [] tmp = x;
            x = y;
            y = tmp;
        }

         int  xIndex = x.length;
         int  yIndex = y.length;
         int  result[] =  new   int [xIndex];
         long  sum =  0 ;

        // Add common parts of both numbers
         while (yIndex >  0 ) {
            sum = (x[--xIndex] & LONG_MASK) + 
                  (y[--yIndex] & LONG_MASK) + (sum >>>  32 );
            result[xIndex] = ( int )sum;
        }

        // Copy remainder of longer number while carry propagation is required
         boolean  carry = (sum >>>  32  !=  0 );
         while  (xIndex >  0  && carry)
            carry = ((result[--xIndex] = x[xIndex] +  1 ) ==  0 );

        // Copy remainder of longer number
         while  (xIndex >  0 )
            result[--xIndex] = x[xIndex];

        // Grow result if necessary
         if  (carry) {
             int  newLen = result.length +  1 ;
             int  temp[] =  new   int [newLen];
             for  ( int  i =  1 ; i<newLen; i++)
                temp[i] = result[i- 1 ];
            temp[ 0 ] = 0x01;
            result = temp;
        }
         return  result;
    }

    /**
     * Multiplies int arrays x and y to the specified lengths and places
     * the result into z.
     */
     private   int [] multiplyToLen( int [] x,  int  xlen,  int [] y,  int  ylen,  int [] z) {
         int  xstart = xlen -  1 ;
         int  ystart = ylen -  1 ;

         if  (z ==  null  || z.length < (xlen+ ylen))
            z =  new   int [xlen+ylen];

         long  carry =  0 ;
         for  ( int  j=ystart, k=ystart+ 1 +xstart; j>= 0 ; j--, k--) {
             long  product = (y[j] & LONG_MASK) *
                           (x[xstart] & LONG_MASK) + carry;
            z[k] = ( int )product;
            carry = product >>>  32 ;
        }
        z[xstart] = ( int )carry;

         for  ( int  i = xstart- 1 ; i >=  0 ; i--) {
            carry =  0 ;
             for  ( int  j=ystart, k=ystart+ 1 +i; j>= 0 ; j--, k--) {
                 long  product = (y[j] & LONG_MASK) * 
                               (x[i] & LONG_MASK) + 
                               (z[k] & LONG_MASK) + carry;
                z[k] = ( int )product;
                carry = product >>>  32 ;
            }
            z[i] = ( int )carry;
        }
         return  z;
    }