namespace pcf{
long long dp[MAXN][MAXM];
unsigned int ar[(MAX >> 6) + 5] = {0};
int len = 0, primes[MAXP], counter[MAX];
void Sieve(){
setbit(ar, 0), setbit(ar, 1);
for (int i = 3; (i * i) < MAX; i++, i++){
if (!chkbit(ar, i)){
int k = i << 1;
for (int j = (i * i); j < MAX; j += k) setbit(ar, j);
}
}
for (int i = 1; i < MAX; i++){
counter[i] = counter[i - 1];
if (isprime(i)) primes[len++] = i, counter[i]++;
}
}
void init(){
Sieve();
for (int n = 0; n < MAXN; n++){
for (int m = 0; m < MAXM; m++){
if (!n) dp[n][m] = m;
else dp[n][m] = dp[n - 1][m] - dp[n - 1][m / primes[n - 1]];
}
}
}
long long phi(long long m, int n){
if (n == 0) return m;
if (primes[n - 1] >= m) return 1;
if (m < MAXM && n < MAXN) return dp[n][m];
return phi(m, n - 1) - phi(m / primes[n - 1], n - 1);
}
long long Lehmer(long long m){
if (m < MAX) return counter[m];
long long w, res = 0;
int i, a, s, c, x, y;
s = sqrt(0.9 + m), y = c = cbrt(0.9 + m);
a = counter[y], res = phi(m, a) + a - 1;
for (i = a; primes[i] <= s; i++) res = res - Lehmer(m / primes[i]) + Lehmer(primes[i]) - 1;
return res;
}
}
using namespace pcf;
long long dp[MAXN][MAXM];
unsigned int ar[(MAX >> 6) + 5] = {0};
int len = 0, primes[MAXP], counter[MAX];
void Sieve(){
setbit(ar, 0), setbit(ar, 1);
for (int i = 3; (i * i) < MAX; i++, i++){
if (!chkbit(ar, i)){
int k = i << 1;
for (int j = (i * i); j < MAX; j += k) setbit(ar, j);
}
}
for (int i = 1; i < MAX; i++){
counter[i] = counter[i - 1];
if (isprime(i)) primes[len++] = i, counter[i]++;
}
}
void init(){
Sieve();
for (int n = 0; n < MAXN; n++){
for (int m = 0; m < MAXM; m++){
if (!n) dp[n][m] = m;
else dp[n][m] = dp[n - 1][m] - dp[n - 1][m / primes[n - 1]];
}
}
}
long long phi(long long m, int n){
if (n == 0) return m;
if (primes[n - 1] >= m) return 1;
if (m < MAXM && n < MAXN) return dp[n][m];
return phi(m, n - 1) - phi(m / primes[n - 1], n - 1);
}
long long Lehmer(long long m){
if (m < MAX) return counter[m];
long long w, res = 0;
int i, a, s, c, x, y;
s = sqrt(0.9 + m), y = c = cbrt(0.9 + m);
a = counter[y], res = phi(m, a) + a - 1;
for (i = a; primes[i] <= s; i++) res = res - Lehmer(m / primes[i]) + Lehmer(primes[i]) - 1;
return res;
}
}
using namespace pcf;