Suppose you want to count the number of ways to represent $$$n$$$ as the sum of $$$k$$$ positive integers. The stars and bars method gives a useful way to represent each such sum.

Write $$$n$$$ stars in a row and place $$$k-1$$$ bars in the gaps between them. The bars divide the stars into $$$k$$$ non-empty groups, and the size of each group is one of the positive integers in the sum.

For example, the string **|*|** represents the ordered tuple $$$(2, 1, 2)$$$, or the sum $$$2 + 1 + 2 = 5$$$. It has $$$5$$$ stars divided into $$$3$$$ non-empty groups, so it represents one way to write $$$5$$$ as a sum of $$$3$$$ positive integers.

Every different placement of the bars gives a different ordered tuple, and every ordered tuple of $$$k$$$ positive integers with sum $$$n$$$ corresponds to exactly one placement. Thus, counting these tuples is equivalent to choosing $$$k-1$$$ gaps for the bars among the $$$n-1$$$ gaps between consecutive stars. This gives $$$\binom{n-1}{k-1}$$$ possible tuples.

In this problem, you are given a valid stars-and-bars string. Write the sum represented by the string as an equation.