VARIABLE SUM Of Values

Using only basic formulas (no VBA then), I need to solve the problem of a VARIABLE SUM of values:

Starting always from the value 1:

- if “control” is “x”: the formula has to write in its “memory” the value 2 and in the next row the new value will be the sum of the two values (1+2), so 3;

- if “control” is “y”: in the next row we repeat 1.

From this point:

- if “x”: we add to the last value of our series another value that will be the last used value and in the next row and in the next row the new value will be the sum of the left value with the right value of the series (in this moment 1+3), so 4;

- if “y”: the formula has to delete from its “memory” the two values that formed the previous sum (in other words the external values of the series) and in the next row the new value will be the sum of the left remained value with the right remained value of the series maintained in “memory”. If remains only a value in the next row we’ll write that single value.

N.B.: if “control” is “z”: the formula must hold in “memory” the sum of values and write that sum in the next row but without considering because all the operation are “suspended”! When “control” will return to “x” or “y” operations of summing or cancelling will start again.

At the end: when everything will restart from the beginning of a new session with the value 1 and “forgetting” entirely what happened above??

There’re 3 cases:

- when all the values are deleted, in the next row will restart a new session with the value 1 “forgetting” entirely what happened above;

- when the result of the sum is >= $A$2, in the next row will restart a new session with the value 1 “forgetting” entirely what happened above;

- when the value of the column “heart” is >= $B$2, in the next row will restart a new session with the value 1 “forgetting” entirely what happened above.

Excuse my english and if you need any clarification… just ask!
No need for this in only a column, you can use all the intermediate columns you may need.
After spending 3 weeks on this I really hope that someone could help me solving this VARIABLE SUM of values.