def solve_2(cap,mod=10**9+7):
f = quad_factor_range(1,0,1,cap+1)
s = 0
for i in xrange(1,cap+1):
comb_factors(f[i-1],f[i+1])
r = 1
for p in f[i-1]:
r = (r * (pow(p,f[i-1][p],mod)+1)) % mod
s += r
while s > mod:
s -= mod
s = (s - i**4-4)%mod
return s
def solve(N,mod=10**9+7):
#Assumes a prime modulus
f,primes = factor_range(N,primes=True)
curr_fact = {p:0 for p in primes}
s = 0
R = 1
mul_dict = {}
for i in xrange(1,N/2+1):
f1 = f[N+1-i] #mult
f2 = f[i] #div
for p in f1:
if p in mul_dict:
mul_dict[p] += f1[p]
else:
mul_dict[p] = f1[p]
for p in f2:
if p in mul_dict:
mul_dict[p] -= f2[p]
else:
mul_dict[p] = -f2[p]
mul = 1
for p in mul_dict:
if curr_fact[p]+mul_dict[p]:
mul = (mul*(pow(p,curr_fact[p]+mul_dict[p],mod)+1))%mod
if curr_fact[p]:
mul = (mul * pow(pow(p,curr_fact[p],mod)+1,mod-2,mod)) % mod
if not mul:
continue
R = (mul*R)%mod
if N%2==0 and 2*i==N:
s = s+R
else:
s = s+2*R
while s > mod:
s -= mod
comb_factors(curr_fact,mul_dict)
mul_dict = {}
return (s+2 - pow(2,N,mod))%mod
