516 - Prime Land

using namespace std;
using ll = long long;
const int PMAX = 1e5 + 11;
bitset<PMAX> is_prime;
vector<int> primes;
int binpow(int base, int exp)
{
    int ans = 1;
    while (exp > 0)
    {
        if (exp & 1)
            ans *= base;
        base *= base;
        exp >>= 1;
    }
    return ans;
}
map<int, int> prime_factors(ll n)
{
    map<int, int> factors;
    ll i = 0, pf = primes[i];
    while (pf * pf <= n)
    {
        while (n % pf == 0)
        {
            factors[pf]++;
            n = n / pf;
        }
        pf = primes[++i];
    }
    if (n != 1)
        factors[n]++;
    return factors;
}
void sieve(void)
{
    is_prime.set();
    is_prime[0] = is_prime[1] = 0;
    for (ll i = 2; i < PMAX; i++)
        if (is_prime[i])
        {
            for (ll j = i * i; j < PMAX; j += i)
                is_prime[j] = 0;
            primes.push_back(i);
        }
}
int main(void)
{
    ios::sync_with_stdio(false), cin.tie(NULL);
    string line;
    sieve();
    while (getline(cin, line) and line[0] != '0')
    {
        stringstream ss(line);
        int n = 1, p, e;
        while (ss >> p >> e)
            n *= binpow(p, e);
        auto factors = prime_factors(n - 1);
        for (auto it = factors.rbegin(); it != factors.rend(); ++it)
        {
            cout << it->first << " " << it->second;
            if (next(it) != factors.rend())
                cout << " ";
        }
        cout << endl;
    }
    return 0;
}