def inv(n, p):
if n == 1:
return 1
a = bezout(n, p)[1]
while a < 0:
a += p
return a
def fx(n, m):
d1 = gcd(n, m)
n0 = n
phin0 = phi2(n)
c = phi2(m) - phin0
if c % d1 != 0:
return 0
c //= d1
m //= d1
n //= d1
v, u = bezout(n, m)
k = (u*c) % m
return n0*k+phin0
def inv(u, p):
return bezout(u, p)[1]
from Tools import decompose_tout, bezout, numpy_sieve
l7 = numpy_sieve(10**7)
a = 1
mod = 1000000087
ss = 0
d = {}
for n in range(2, 10**7 + 1):
lp = decompose_tout(n, l7)
for p, i in lp:
if p in d:
a *= bezout(mod, 1 + 2 * d[p])[0]
d[p] += i
a *= 1 + 2 * d[p]
else:
d[p] = i
a *= 1 + 2 * d[p]
a %= mod
ss += a
ss %= mod
print(ss)
# sol = 416146418
# %% Problem 506
from Tools import bezout
L = [(123432, 0, 0), (123432, 1, 1), (23432, 12, 2), (3432, 123, 3), (432, 1234, 4), (32123432, 0, 0), (123432, 123, 3),
(432, 12343, 5), (2123432, 123, 3), (432123432, 0, 0), (123432, 1234, 4), (32123432, 123, 3), (432123432, 12, 2),
(3432123432, 1, 1), (23432123432, 0, 0)]
L_q0_r = [0, 1, 2, 3, 4, 32, 123, 43, 2123, 432, 1234, 32123, 43212, 34321, 23432]
NN = 1000
N, R = int.__divmod__(NN, 15)
mod = 123454321
u, v = bezout(9, mod) # 1 = 9*v+u*mod
while v < 0:
v += mod
inv_9 = v
u2, v = bezout(999999, mod) # 1 = 9*v+u*mod
while v < 0:
v += mod
inv_9_6 = v
def v(n):
q, r = int.__divmod__(n, 15)
a, b, lb = L[r]
s = b+123432*inv_9_6*(pow(10**6, q-1, mod)-1)*10**lb + pow(10, 6*q-6+lb, mod)*a
return s % mod
def inv(a, p):
return bezout(a, p)[1] % p