Use array in a dynamic statement

Hi,

I am trying to implement a PL/PgSQL function as following:
CREATE OR REPLACE FUNCTION sort_by_d_idx (nids INT[][], tbl_name VARCHAR)
RETURNS varchar[]
AS $$
DECLARE
result varchar[];
BEGIN

EXECUTE 'SELECT ARRAY(SELECT t.idx FROM generate_series(array_lower($1,1), array_upper($1,1)) AS s(i), '
||tbl_name||' t WHERE $1[s.i][1] = t.rid and $1[s.i][2] = t.rtid ORDER BY length(t.idx))'
INTO result;

RETURN result;
END;
$$ LANGUAGE plpgsql;

I got an error "ERROR: there is no parameter $1" when I test the function with:
select sort_by_d_idx('{{8148, 1}, {8149, 1}, {300, 2}, {8163, 1}, {8170, 1}}'::int[][], 'd_tree_1');

The error is understandable, but my question is how to supply the int[][] array into the dynamic SQL?

To help understand the dynamic statement, the structure of d_tree_1 is (rid, rtid, idx). The PK is (rid, rtid) pair.

If the tbl_name is fixed, the following function works well:
CREATE OR REPLACE FUNCTION sort_by_d_idx2 (nids INT[][])
RETURNS varchar[]
LANGUAGE SQL
AS $$
SELECT ARRAY(
SELECT t.idx
FROM
generate_series(array_lower($1,1), array_upper($1,1)) AS s(i), d_tree_1 t
WHERE $1[s.i][1] = t.rid and $1[s.i][2] = t.rtid
ORDER BY length(t.idx)
);
$$;

Unfortunately, the tbl_name is determined at query time.

Please help.