def solve():
"""
http://en.wikipedia.org/wiki/Partition_(number_theory)
"""
from prime import divisors_sigma
p = [1]
for n in range(1,N+1):
p.append( 1./n*sum(divisors_sigma(n-k)*p[k] for k in range(0,n)) )
return int(p[-1]-1)
def slow():
"""
http://en.wikipedia.org/wiki/Partition_(number_theory)
"""
from prime import divisors_sigma
p = [1]
n = 1
while True:
p.append( 1./n*sum(divisors_sigma(n-k)*p[k] for k in range(0,n)) )
#print n, p[-1]
if n > 1 and p[-1]%N == 0:
break
n += 1
return n, int(p[-1])
