shell script nested loop to copy files

Question

for i in 2 4 8 16
do
         for j in 100 1000 10000 100000 1000000
         do
                 cp foo.c bar_$i_$j.c
         done
done

I have this nested loop. The output I expected is

bar_2_100.c
bar_2_1000.c
bar_2_10000.c
bar_2_100000.c
bar_2_1000000c.
bar_4_100.c
bar_4_1000.c
bar_4_10000.c
bar_4_100000.c
bar_4_1000000c.
...

But I didn't get $i part of loop. My output is

bar_100.c
bar_1000.c

and so on. How can I copy the similar name by using nested loop in shell script?