int main(){
vsip_init((void*)0);
acos_f();
asin_f();
atan2_f();
atan_f();
cos_f();
sin_f();
sqrt_f();
tan_f();
ceil_f();
exp_f();
exp10_f();
floor_f();
fmod_f();
hypot_f();
log_f();
log10_f();
mag_f();
max_f();
min_f();
pow_f();
rsqrt_f();
sinh_f();
tanh_f();
cosh_f();
arg_f();
cadd_f();
cdiv_f();
cexp_f();
cjmul_f();
cmul_f();
clog_f();
cmag_f();
cmagsq_f();
cmplx_f();
cneg_f();
conj_f();
crecip_f();
csqrt_f();
csub_f(0);
imag_f();
real_f();
polar_f();
rect_f();
vsip_finalize((void*)0);
return 0;
}
void main() {
R = SqrRoot(m);
int cnt = 0;
for (long i = 1; m / i > R; ++i)
basis[++cnt] = m / i;
for (int i = R; i; --i)
basis[++cnt] = i;
// for (int i = 1; i <= cnt; ++i) {
// if (get_index(basis[i]) != i)
// print("!!! {} {}\n", get_index(basis[i]), i);
// }
for (int i = 1; i <= cnt; ++i) {
num_primes[i] = basis[i] - 1;
}
// for (int i = 1; i < cnt; ++i) {
// for (int v = basis[i + 1] + 1; v <= basis[i]; ++v)
// if (v > R && ProbPrime(v))
// f[basis[i]] += 2;
// }
// f[1] = 1;
// for (int i = cnt - 1; i; --i) {
// f[basis[i]] += f[basis[i + 1]];
// // print("init {} = {}\n", basis[i], f[basis[i]]);
// }
// long ans = 0;
// for (int i = 1; i <= m; ++i) {
// ans += m / i;
// }
// print("bf = {}\n", ans);
for (long x = 2; x <= R; ++x) {
if (ProbPrime(x)) {
print("current = {}\n", x);
for (int i = 1; i <= cnt; ++i) {
long y = basis[i];
if (x * x > y)
break;
auto a = num_primes[get_index(y / x)];
auto b = num_primes[get_index(x - 1)];
num_primes[i] -= a - b;
}
}
}
for (int i = 1; i <= cnt; ++i) {
num_primes[i] %= MOD;
// print("{} {}\n", basis[i], num_primes[i]);
}
for (int i = 1; i <= cnt; ++i) {
f[i] = 1;
// if (basis[i] >= R) {
// f[i] += 2 * (num_primes[get_index(basis[i])] - num_primes[R]);
// }
// print("init {} {}\n", basis[i], f[i]);
}
for (long p = R; p; --p) {
if (ProbPrime(p)) {
print("current = {}\n", p);
int t = p > n ? 0 : get_power(p, n);
for (int e = 0; e <= 60; ++e)
g[e] = (e + 1) * (t + 1) + t * (t + 1) / 2;
for (int i = 1; i <= cnt; ++i) {
long y = basis[i];
if (t == 0 && p * p > y)
break;
long v = 0; // 2 * (num_primes[get_index(y)] - num_primes[p]);
for (int e = 0; y; ++e) {
v += real_f(y, p) * g[e] % MOD;
y /= p;
}
if (basis[i] >= p)
v -= 2 * (num_primes[i] - num_primes[get_index(p)] + 1) % MOD;
f[i] = (v + MOD) % MOD;
// print("update {} = {}\n", basis[i], v);
}
}
}
print("ans = {}\n", real_f(m, 1));
}
