Ampersandwich: A very Special Sudoku Sandwich

Today's Puzzle:

A tough but incredible puzzle from LMDemasi, a very tasty puzzle in fact!

Link to Play Along:

Ampersandwich by LMDemasi http://tinyurl.com/SudokuSleuthAmpersandwich

Rules:

Regular Sudoku rules apply - Place the digits 1 - 9 in each row, column, and box.

Sandwich - A number outside the grid indicates the sum of the numbers between 1 and 9 in that row or column.

Non-repeating Between Lines - Cells along lines between two circles must have values between those in the circles. Digits may not repeat along a line.