Each cell in a grid contains one of the digits from 1 to 7. Each row and column has each digit exactly once. The following clues give the totals of the cells indicated. How can you fill the grid?

A56=13
ABC1=6
ABCD4=13
B234=18
BC7=5
C34=4
D67=13
DEF2=8
EFG3=16
EF5=6
FG5=4
G1234=17