factovisors.cpp

// Michael Pfeifer
// Version 04, 2018/02/17

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

typedef long long ll;
typedef long double ld;
typedef unsigned int uint;
typedef unsigned long long ull;

const ld  pi   = 4.0*atanl(1.0);
const int iinf = 1e9 + 10;
const ll  inf  = 1e18 + 10;
const int mod  = 1000000007;
const ld  prec = .000001;

#define enld endl
#define endl '\n'
#define pb push_back
#define debug(x) cout<<#x<<" -> "<<x<<'\n'
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define uni(x) (x).erase(unique(all(x)), (x).end())
#define rep(i, n) for (ll i = 0; i < (ll)(n); ++i)
#define rep1(i, n) for (ll i = 1; i <= (ll)(n); ++i)
#define umap unordered_map
#define uset unordered_set

template<class TIn>
using indexed_set = tree<
        TIn, null_type, less<TIn>,
        rb_tree_tag, tree_order_statistics_node_update>;

void fast() {
    ios::sync_with_stdio(false);
    cin.tie(NULL); cout.tie(NULL);
}

void file() {
    auto a = freopen("a.in",  "r", stdin);
    auto b = freopen("a.out", "w", stdout);
    if(!a || !b) cout << "uh oh" << endl;
}





map<ll,ll> factorization(ll n) {
    map<ll,ll> fac;
    for(ll i = 2; i <= sqrt(n); i++) {
        while(n % i == 0) {
            n /= i;
            fac[i]++;
        }
    }
    if(n > 1) {
        fac[n]++;
    }
    return fac;
}

bool solve(ll n, ll m) {
    map<ll,ll> factors = factorization(m);

    map<ll,ll> taken;

    for(auto& i : factors) {
        int idx = i.first;
        while(i.second > 0) {
            if(idx > n) {
                break;
            }
            if(taken[idx] == 0) {
                taken[idx] = 1;
            }
            while((idx / taken[idx]) % i.first == 0) {
                taken[idx] *= i.first;
                i.second--;
                if(i.second == 0) {
                    break;
                }
            }

            idx += i.first;
        }
    }

    bool works = true;
    for(auto i : factors) {
        if(i.second > 0) {
            works = false;
        }
    }

    return works;
}

int main() {
    //file();
    fast();

    ll n, m;
    while(cin >> n && cin >> m) {
        bool works = solve(n,m);
        if(m == 0) {
            works = false;
        }
        if(works) {
            cout << m << " divides " << n << "!" << endl;
        }
        else {
            cout << m << " does not divide " << n << "!" << endl;
        }
    }

    return 0;
}