Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/4
M:6/4
K:F
['A F']  
X:1
L:1/4
M:6/4
K:F
 F, F A/B/ c f2 | F, F A/B/ c B G | F, F A/B/ c f2 | g G G, B A G | C, c e c g2 | 
 c d/e/f/e/ d/c/ B G | C, c e c g e/f/ | g G G, B A G | A F F, c A F | A F F, c B G | 
 A F F, c A F | c G G, B A G ||  