Amazons database doesn't support very large numbers, so numbers are stored as a string of binary characters, $\text{'}$O$\text{'}$ and $\text{'}1\text{'}.$ Accidentally, a $\text{'}!\text{'}$ was entered at some positions and it is unknown whether they should be $\text{'}$O$\text{'}$ or $\text{'}1\text{'}.$ The string of incorrect data is made up of the characters $\text{'}$O$\text{'},\text{'}1\text{'}$ and $!$ where $!\text{'}$ is the character that got entered incorrectly. $\text{'}!\text{'}$ can be replaced with either $\text{'}$O$\text{'}$ or $\text{'}1\text{'}.$ Due to some internal faults, some errors are generated every time O$\text{'}$ and $\text{'}1\text{'}$ occur together as $\text{'}01\text{'}$ or $\text{'}10\text{'}$in any subsequence of the string. It is observed that the number of errors a subsequence $\text{'}01\text{'}$ generates is x$,$ while a subsequence $\text{'}10\text{'}$ generates y errors. Determine the minimum total errors generated. Since the answer can be very large, return it modulo $10\backslash$deg $+7.$ For example, given string errorString $="101!1",$ x $=2,$ y$=3,$ If the $!\text{'}$at index $3$ is replaced with $\text{'}$O$\text{'},$ the string is $"10101".$ The number of times the subsequence $01$ occurs is $3$ at indices $(1,2),(1,4),$ and $(3,4).$ The number of times the subsequence $10$ occurs is also $3,$ indices $(0,1),(0,3)$ and $(2,3).$ The number of errors is $3*$x$+3*$ y $=6+9=15.$ If the $!\text{'}$ is replaced with $\text{'}1\text{'},$ the string is $"10111".$ The subsequence $01$ occurs $3$ times and$10$ occurs $1$ time. The number of errors is $3*$x $+$ y $=9.$ The minimum number of errors is min$(9,15)$ modulo $109+7=9$