def comb_squarefree(n,k):
global primes
for p in primes:
t = pe.prime_fact_ord(p,n)-pe.prime_fact_ord(p,n-k)-pe.prime_fact_ord(p,k)
if t > 1:
return 0
return 1
def s(p, e):
"""
returns the minimum n with p^e | n!
"""
if e < p:
return p*e
i = p
while True:
if prime_fact_ord(p, p*i) >= e: return p*i
i += 1
from proj_euler import gcd,prime_fact_ord
from bisect import bisect_right
h = []
cap = 10**12
mod = 10**5
t = 1
while t <= cap:
t5 = 1
while t*t5 <= cap:
h.append(t*t5)
t5 *= 5
t *= 2
o2 = prime_fact_ord(2,cap)
o5 = prime_fact_ord(5,cap)
exp2 = o2-o5 #Significant exponent of 2 in final product
h = sorted(h) #numbers divisible only by 2 and 5
print len(h)
res = 1 #init to one
for i in xrange(1,min(cap+1,mod)):
if gcd(i,10) == 1:
e = 0 #the exponent by i in the final product
for m in h:
if m*i > cap:
break
max_r = ((cap/m) - i) / mod #maximum r with m*(r*mod+i) <= cap
e += max_r+1
res = (res * pow(i,e,mod)) % mod