diff --git a/06-hash/hash.tex b/06-hash/hash.tex
index 5c2ecdab338720466967f4831dd0ff86d0f1261e..b17277b261b789058f3e80895bf7bfaee171a2cf 100644
--- a/06-hash/hash.tex
+++ b/06-hash/hash.tex
@@ -635,6 +635,10 @@ $f$,~$g$ chosen at random from a~$\lceil 6\log n\rceil$-independent family.
 Then the expected time complexity of \alg{Insert} is $\O(1)$.
 }
 
+\note{
+Setting the timeout to $\lceil 6\log m\rceil$ also works.
+}
+
 \note{
 It is also known that a~6-independent family is not sufficient to guarantee
 expected constant insertion time, while tabulation hashing (even though
diff --git a/08-string/string.tex b/08-string/string.tex
index c115c81f132780fde01f66d2a86661df380c57de..a2ccb5e10d6a2717d27d4054864290515ee70863 100644
--- a/08-string/string.tex
+++ b/08-string/string.tex
@@ -96,13 +96,16 @@ where $\LCP(\gamma,\delta)$ is the maximum~$k$ such that $\gamma[{}:k] = \delta[
 \obs{The LCP array can be easily used to find the longest common prefix of any two
 suffixes $\alpha[i:{}]$ and $\alpha[j:{}]$. We use the rank array to locate them
 in the lexicographic order of all suffixes: they lie at positions
-$i' = R[i]$ and $j' = R[j]$. Then we compute $k = \min(L[i'], L[i'+1], \ldots, L[j'-1])$.
+$i' = R[i]$ and $j' = R[j]$ (w.l.o.g. $i' < j'$).
+Then we compute $k = \min(L[i'], L[i'+1], \ldots, L[j'-1])$.
 We claim that $\LCP(\alpha[i:{}], \alpha[j:{}])$ is exactly~$k$.
 
 First, each pair of adjacent suffixes in the range $[i',j']$ has a~common prefix of
 length at least~$k$, so our LCP is at least~$k$. However, it cannot be more:
 we have $k = L[\ell]$ for some~$\ell \in [i',j'-1]$, so the $\ell$-th and $(\ell+1)$-th suffix
-differ at position $k+1$. Since all suffixes in the range share the first~$k$ characters,
+differ at position $k+1$ (or one of the suffixes ends at position~$k$, but we can simply
+imagine a~padding character at the end, ordered before all ordinary characters.)
+Since all suffixes in the range share the first~$k$ characters,
 their $(k+1)$-th characters must be non-decreasing. This means that the $(k+1)$-th character
 of the first and the last suffix in the range must differ, too.
 }