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:G
['B A G']  
X:1
L:1/4
M:6/4
K:G
"^Refrain""G" G3"D" A3 | D3/2 E/ F"Am" E2 D |"G" G2 A B3/2 c/ B |"Am" A2 E"D" A3 | g"G" G3"D" A3 | 
 D3/2 E/ F"Am" E2 D |"G" E2 F G3/2 c/ B |"D" A G F"G" G2 g"^Verse" .B | B3/2 A/ B G A B | 
"C" (c3 c) d c |"Em" B3/2 A/ B B A G |"D" A3- A2 (D/=C/) | a Te e Te"Em" G2 A B2 c | 
"G" d2 G"D" F2 D |"G" d2 G"D" F2 D |"G" d2 G (F E) D | (e f) u_e g G"Em" G2 A B3/2 c/ B | 
"D" A G F"G" G3 |]  