Seemingly simple but actually difficult?

I want a sumif formula that sums the target range if any of the cells
matched are not blank, if all of the cells matched are blank then it
should return a blank (and not a 0). If the sum range does have any
values (including 0!) then it should return the sum.

Example

Col to Match Col to Sum
A B
1
2 23
1
1
3 0
3

So in column C I need my sumif formula. It should return BLANK for all
rows with 1 in column A, 23 for row 2 and 0 for all rows with a 3 in
column A.


Any ideas?