Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/2=100
M:2/2
K:C
['c4 B>c d>BG>B d2 cd', 'G2 e>f']  
X:1
L:1/8
Q:1/2=100
M:2/2
K:C
 G>E | C2"^*" c4 B>c | d>BG>B d2 cd | e>ce>c f>df>d | gece d2{B} G>E | C2 c4 B>c | d>BG>B d2 cd | 
 ecdB c>AG>F | G2 G2 G2 :: e>f | g>fe>d c>BA>G | A2 F2 F2 f>g | a>gf>e d>cB>A | B2 G2 G2 e>f | 
 gege fafa | gege fafa | g>fa>f edcB | c2 c2 c2 :|  