Begin implementation of better partition strategy

Uneven folios are awkward, and folios of many different sizes are
hard to bind correctly. Therefore, try to partition the sheets as
folios of max_folio_size and max_folio_size - k, where k is minimal.

foliator.py

@@ -34,6 +34,30 @@ def append_folio_A6(input_pdf, offset, size, append_to):
         dpage.merge_page(ipage)
     return writer
 
+# Tries to find a partition as
+# num_sheets = max_folio_size * a + (max_folio_size - k) * b
+# where k is minimal. We let n = max_folio_size and L = num_sheets.
+# Note that when L > n^2, then k = 1 must succeed.
+def find_partition(num_sheets, max_folio_size):
+    max_a = num_sheets // max_folio_size
+    for k in range(1, max_folio_size):
+        # We want to solve a*k = L (mod n-k). This happens iff
+        # a*k' = L' (mod m') where k,L,m are divided by their gcd.
+        # Then, if k' and m' have a common factor, L' doesn't have it and there
+        # are no solutions. Otherwise, there's one solution mod m'.
+        g = math.gcd(max_folio_size - k, k, num_sheets)
+        mprime = (max_folio_size - k)//g
+        kprime = k//g
+        Lprime = num_sheets//g
+        if (math.gcd(kprime, mprime) > 1):
+            continue
+        a_mod_mprime = (pow(kprime, -1, mprime) * Lprime) % mprime
+        tosub = (max_a - a_mod_mprime + mprime) % mprime
+        # If we're a bit above, substract only a little. But a bit below implies
+        # substracting almost mprime.
+        candidate = max_a - tosub
+        if (candidate >= 0):
+            return (candidate, k)
 
 # Interprets input_pdf as a list of A6 pages, and appends to append_to with
 # A5 pages using the following rules: