Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:F
['Accc dccc']  
X:1
L:1/8
M:4/4
K:F
 a2 |"C" g3 f"C7" e2 d2 |"F" cdcB A2 G"^3"F |"C" ECEG"C7" cdcB |"F" AFAc f2 a2 | 
"C" g3 f"C7" e2 d2 |"F" cdcB A2 GF |"C7" EFGA Bcde |"F" f2 a2 f2 :: cB |"F" Accc dccc | Acfc acfc | 
"F" Accc dccc | Acfc acfc |"F" Accc dccc |"C" =Bcec gc_bc | =Bcec gc_bc |"C7" acgc"F" f2 :|  