# Problem 555: McCarthy 91 function
The McCarthy 91 function is defined as follows: \$\$ M\_{91}(n) =
\\begin{cases} n - 10 & \\text{if } n > 100 \\\\
M\_{91}(M\_{91}(n+11)) & \\text{if } 0 \\leq n \\leq 100 \\end{cases}
\$\$ We can generalize this definition by abstracting away the constants
into new variables: \$\$ M\_{m,k,s}(n) = \\begin{cases} n - s &
\\text{if } n > m \\\\ M\_{m,k,s}(M\_{m,k,s}(n+k)) & \\text{if } 0
\\leq n \\leq m \\end{cases} \$\$ This way, we have \$M\_{91} =
M\_{100,11,10}\$. Let \$F\_{m,k,s}\$ be the set of fixed points of
\$M\_{m,k,s}\$. That is, \$\$F\_{m,k,s}= \\left\\{ n \\in \\mathbb{N}
\\, | \\, M\_{m,k,s}(n) = n \\right\\}\$\$ For example, the only fixed
point of \$M\_{91}\$ is \$n = 91\$. In other words, \$F\_{100,11,10}=
\\{91\\}\$. Now, define \$SF(m,k,s)\$ as the sum of the elements in
\$F\_{m,k,s}\$ and let \$S(p,m) = \\displaystyle \\sum\_{1 \\leq s <
k \\leq p}{SF(m,k,s)}\$. For example, \$S(10, 10) = 225\$ and \$S(1000,
1000)=208724467\$. Find \$S(10\^6, 10\^6)\$.