Cages a la Mod

- Normal sudoku rules apply: every row, column, and box must contain a complete set of the digits 1-9. - Cages: Digits in a cage indicated by a dashed line must sum to the total shown in the upper left corner of the cage, if given. Digits cannot repeat within a cage. Modular Lines: every set of three sequential digits along a teal Modular line contains digits with three different remainders when divided by 3. Digits on two-cell lines must have different remainders when divided by 3. Digits may repeat on a line if allowed by other rules. Kropki dots: Digits separated by a peach Kropki dot are in a k:1 ratio, with k a whole number to be determined by the solver. The value of k may be different for different dots.