Calculate the date of the FIRST MONDAY of a month from a known start date

Generally the following formula (copied from a thread , here, that is over 10 years old and now closed) works fine but then blows its brains out in certain years!

DATE(YEAR(A13),MONTH(A13),7-1+(MOD(3+7-WEEKDAY(DATE(YEAR(A13),MONTH(A13),1)),7)))

but it does not consistently and accurately return the correct date for the first Monday of the month where B36 contains the value 1/8/2043 (dd/mm/yyyy)

I get the correct day show above by tweaking the formula to read

DATE(YEAR(A13),MONTH(A13),1-1+(MOD(3+7-WEEKDAY(DATE(YEAR(A13),MONTH(A13),1)),7)))

Cell A13 changes relative to each column as the year changes (A13,B13,C13,D13)

but then I do not consistently get the correct date for the first Monday of August where the date changes by column by one year until 2046. I

For example 2045 gives the date as 31 July 2045 (a Monday but the wrong month!)

Any idea about how to fix this so that EVERY year correctly returns the correct date for the first Monday of August?

Greatly appreciate the assistance!