//no even number in the table
void factor_using_table_odd(i64 n, IntPairVec& vpairs, const vector<int>& ftable)
{
vpairs.clear();
i64 n2 = 0;
while( (n & 1) == 0){
n >>= 1;
++n2;
}
if(n2)
vpairs.push_back(IntPair(2, n2));
assert( (n & 1) > 0);
int np = (n-1) >> 1;
int pwr = 0;
int curr_fac = ftable[np];
while(curr_fac>1){
++pwr;
n /= curr_fac;
np = (n-1) >> 1;
while(curr_fac == ftable[np]){
++pwr;
n /= ftable[np];
np = (n-1) >> 1;
}
vpairs.push_back(IntPair(curr_fac, pwr));
curr_fac = ftable[np];
pwr = 0;
}
}
//the factors are from small to large
//first is prime number, second is power
void factor_using_table(i64 n, IntPairVec& vpairs, const vector<int>& ftable)
{
vpairs.clear();
int pwr = 0;
int curr_fac = ftable[n];
while(curr_fac>1){
++pwr;
n /= ftable[n];
while(curr_fac == ftable[n]){
++pwr;
n /= ftable[n];
}
vpairs.push_back(IntPair(curr_fac, pwr));
curr_fac = ftable[n];
pwr = 0;
}
}
