assert (k > 0);
while (--k > 0)
  {
    struct tavl_node *y = pa[k];

    if (da[k] == 0)
      {
        y->tavl_balance++;
        if (y->tavl_balance == +1)
          break;
        else if (y->tavl_balance == +2)
          {
            struct tavl_node *x = y->tavl_link[1];
            assert (x != NULL);
            if (x->tavl_balance == -1)
              {
                struct tavl_node *w;

                assert (x->tavl_balance == -1);
                w = x->tavl_link[0];
                x->tavl_link[0] = w->tavl_link[1];
                w->tavl_link[1] = x;
                y->tavl_link[1] = w->tavl_link[0];
                w->tavl_link[0] = y;
                if (w->tavl_balance == +1)
                  x->tavl_balance = 0, y->tavl_balance = -1;
                else if (w->tavl_balance == 0)
                  x->tavl_balance = y->tavl_balance = 0;
                else /* |w->tavl_balance == -1| */
                  x->tavl_balance = +1, y->tavl_balance = 0;
                w->tavl_balance = 0;
                if (w->tavl_tag[0] == TAVL_THREAD)
                  {
                    y->tavl_tag[1] = TAVL_THREAD;
                    y->tavl_link[1] = w;
                    w->tavl_tag[0] = TAVL_CHILD;
                  }
                if (w->tavl_tag[1] == TAVL_THREAD)
                  {
                    x->tavl_tag[0] = TAVL_THREAD;
                    x->tavl_link[0] = w;
                    w->tavl_tag[1] = TAVL_CHILD;
                  }
                pa[k - 1]->tavl_link[da[k - 1]] = w;
              }
            else if (x->tavl_balance == 0)
              {
                y->tavl_link[1] = x->tavl_link[0];
                x->tavl_link[0] = y;
                x->tavl_balance = -1;
                y->tavl_balance = +1;
                pa[k - 1]->tavl_link[da[k - 1]] = x;
                break;
              }
            else /* |x->tavl_balance == +1| */
              {
                if (x->tavl_tag[0] == TAVL_CHILD)
                  y->tavl_link[1] = x->tavl_link[0];
                else
                  {
                    y->tavl_tag[1] = TAVL_THREAD;
                    x->tavl_tag[0] = TAVL_CHILD;
                  }
                x->tavl_link[0] = y;
                x->tavl_balance = y->tavl_balance = 0;
                pa[k - 1]->tavl_link[da[k - 1]] = x;
              }
          }
      }
    else
      {
        y->tavl_balance--;
        if (y->tavl_balance == -1)
          break;
        else if (y->tavl_balance == -2)
          {
            struct tavl_node *x = y->tavl_link[0];
            assert (x != NULL);
            if (x->tavl_balance == +1)
              {
                struct tavl_node *w;

                assert (x->tavl_balance == +1);
                w = x->tavl_link[1];
                x->tavl_link[1] = w->tavl_link[0];
                w->tavl_link[0] = x;
                y->tavl_link[0] = w->tavl_link[1];
                w->tavl_link[1] = y;
                if (w->tavl_balance == -1)
                  x->tavl_balance = 0, y->tavl_balance = +1;
                else if (w->tavl_balance == 0)
                  x->tavl_balance = y->tavl_balance = 0;
                else /* |w->tavl_balance == +1| */
                  x->tavl_balance = -1, y->tavl_balance = 0;
                w->tavl_balance = 0;
                if (w->tavl_tag[0] == TAVL_THREAD)
                  {
                    x->tavl_tag[1] = TAVL_THREAD;
                    x->tavl_link[1] = w;
                    w->tavl_tag[0] = TAVL_CHILD;
                  }
                if (w->tavl_tag[1] == TAVL_THREAD)
                  {
                    y->tavl_tag[0] = TAVL_THREAD;
                    y->tavl_link[0] = w;
                    w->tavl_tag[1] = TAVL_CHILD;
                  }
                pa[k - 1]->tavl_link[da[k - 1]] = w;
              }
            else if (x->tavl_balance == 0)
              {
                y->tavl_link[0] = x->tavl_link[1];
                x->tavl_link[1] = y;
                x->tavl_balance = +1;
                y->tavl_balance = -1;
                pa[k - 1]->tavl_link[da[k - 1]] = x;
                break;
              }
            else /* |x->tavl_balance == -1| */
              {
                if (x->tavl_tag[1] == TAVL_CHILD)
                  y->tavl_link[0] = x->tavl_link[1];
                else
                  {
                    y->tavl_tag[0] = TAVL_THREAD;
                    x->tavl_tag[1] = TAVL_CHILD;
                  }
                x->tavl_link[1] = y;
                x->tavl_balance = y->tavl_balance = 0;
                pa[k - 1]->tavl_link[da[k - 1]] = x;
              }
          }
      }
  }
