def P(f,r):
if f == 1:
return r*(r+1) / 2
k = (r-1)/2
b = [(f*f) / 2]
nextSquare = 2*(f/2)+1
b.append((nextSquare)**2 - b[0])
b.append((nextSquare+1)**2 - b[1])
if r <= 3:
return b[r-1]
else:
if not r%2:
a = b[2] - b[0] + 2
return b[1] + pe.arithmetic(a,4,k)
else:
a = b[2] - b[0]
return b[0] + pe.arithmetic(a,4,k)
def F(n,k=1): global c1,c2,sq,mod,max_cache,totSum if n == 1: return 1 if n < max_cache: return totSum[n] if n <= sq and c2[n]: return c2[n] if k <=sq and c1[k]: return c1[k] s = G(n,mod) # print s,n q,div = n/2,2 while q >= 1: r = n % div div_next = div + r/q + 1 s = ( s - (arithmetic(div,1,div_next-div)%mod) * F(n/div,k*div)) % mod div = div_next q = n/div_next if n <= sq: c2[n] = s if k <=sq: c1[k] = s return s