def fund(n):
lower, upper = bounds(n)
p = 0
for b in range(lower, upper+1):
r = n - b
for seq in mtools.comb(range(1,n+1), r):
a = mtools.mul(seq)
p += a
return mtools.fac(n+1)/p
def get_n(l):
l2 = [primes[i]**x for (i, x) in enumerate(l)]
return mtools.mul(l2)
def search(l, (m, n)):
states = [l]
visited = {}
nm = 0
dm = em = 1
while True:
s = states.pop(0)
h = hashable(s)
try:
if visited[h]:
continue
except KeyError:
visited[h] = True
ps = [primes[i] for i in range(len(s))]
pm = mtools.mul(ps)
pm1 = mtools.mul([p-1 for p in ps])
d = get_n(s)
e1, d1 = normalize(d*pm1, (d-1)*pm)
if e1*n < d1*m:
return d
if e1*dm < d1*em:
em = e1
dm = d1
nm = d
elif d > nm:
continue
states += expand_states(s)
states.sort(cmp = lambda x,y: cmp(get_n(x), get_n(y)))
def normalize(e, d):
def f(l):
l2 = [2*x+1 for x in l]
return (mtools.mul(l2)+1)/2
