Krosscut Knights

Normal sudoku rules apply.

Cells separated by a chess knight's move cannot contain the same digit.

Digits along an arrow must sum to the value in the attached circle. Digits may repeat on arrows if allowed by other rules.

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 are to be determined by the solver. They do not share cells and neither path appears on an arrow or circle.