Crossed Paths

Normal sudoku rules apply.

Digits in cages do not repeat, and must sum to the small clue in the top left corner.

A path consisting of the digits 1 to 9, in order, crosses from left to right across the grid with each digit in its corresponding column (1 in column 1, 2 in column 2, etc.) The cells along the path are connected orthogonally or diagonally.

A similar path crosses the grid from top to bottom, starting with a 1 in row 1, then a 2 in row 2, ending with a 9 in row 9. Again, cells along the path are connected orthogonally or diagonally.

The paths (which do not share cells, nor appear in any cage) are to be determined by the solver.