4. A square piece of paper is cut into two parts along a straight line that does not pass through any vertex; take one of the parts and cut it into two parts along a straight line that does not pass through any vertex; then take one of the resulting three parts and cut it into two parts along a straight line that does not pass through any vertex... and so on. In the end, 34 hexagons and some other polygonal pieces are obtained. The minimum number of cuts required is ( ).
(A) 2004
(B) 2005
(C) 2006
(D) 2007