With two straight cuts, we can divide a flat pancake into four pieces: [asy]
size(4cm);
draw(Circle((0,0),1));
draw(rotate(45)*(1,0)--rotate(200)* (1,0),dashed);
draw(rotate(150)*(1,0)--rotate(330) *(1,0),dashed);
[/asy]
What is the fewest number of straight cuts that will divide a flat pancake into $16$ pieces? (The pieces do not need to be the same shape or size.)