Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:1/4=160
M:4/4
K:C
['E D2 E2', 'E6 z E', 'g/^f/g dd _ee']  
X:1
L:1/8
Q:1/4=160
M:4/4
K:C
 E |:"G" D2 GG"C" E2 FE |"G" DC-CD"C" E4 | EA GG"G7" E2 FF |"C" E6 z E ::"G" D2 GG G2 G2 | 
 G2 B2 BA AG |"Am" A3 D"G" GFED |1"C" E6 z E :|2"C" !fermata!E4 z e/f/ g/^f/g |:[M:2/4]"C" aa fe | 
 ee/f/ g/^f/g | aa fe | ee/f/ g/^f/g |"Dm" dd _ee | c e/f/ g/^f/g |"G" dd _ee |1 
"C" c e/f/ g/^f/g :|  