How do you cut your sandwich?

Standard sudoku rules apply: each row, column, and 3x3 box must contain all the digits from 1 to 9.

Clues outside the grid are sandwich clues with a twist: in the appropriate row or column, digits between the 1 and the 9 must sum to the value of the clue. In addition, for each diagonal from the clue (of length at least 2), the digits between the first instance of each of 9 and 1 (as seen from the clue) must sum to the value of the clue.