Codeforces-solutions/Codeforces Round 843 (Div. 2)/D. Friendly Spiders.cpp

/* Problem URL: https://codeforces.com/problemset/problem/1775/D */

#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;

template <class T, class comp = less<>>
using ordered_set = tree<T, null_type , comp , rb_tree_tag , tree_order_statistics_node_update>;

#define V vector

#define rmin(a, b) a = min(a, b)
#define rmax(a, b) a = max(a, b)

#define rep(i, lim) for (int i = 0; i < (lim); i++)
#define nrep(i, s, lim) for (int i = s; i < (lim); i++)

#define repv(i, v) for (auto &i : (v))
#define fillv(v) for (auto &itr_ : (v)) { cin >> itr_; }
#define sortv(v) sort(v.begin(), v.end())
#define all(v) (v).begin(), (v).end()

using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;

using ll = long long;

using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;

template<class v>
auto operator<<(ostream &os, const vector<v> &vec)->ostream& {
    os << vec[0];
    for (size_t i = 1; i < vec.size(); i++) {
        os << ' ' << vec[i];
    }
    os << '\n';
    return os;
}

template<class v>
auto operator>>(istream &is, vector<v> &vec)->istream& {
    for (auto &i : vec) {
        is >> i;
    }
    return is;
}

template<class v>
auto operator<<(ostream &os, const vector<vector<v>> &vec)->ostream& {
    for (auto &i : vec) {
        os << i[0];
        for (size_t j = 1; j < i.size(); j++) {
            os << ' ' << i[j];
        }
        os << '\n';
    }
    return os;
}

template<class v>
auto operator>>(istream  &is, vector<vector<v>> &vec)->istream& {
    for (auto &i : vec) {
        for (auto &j : i) {
            is >> j;
        }
    }
    return is;
}

const int oo = INT32_MAX >> 1;
const ll OO = INT64_MAX >> 1;

const int MAXN = 3e5 + 1;

vi primes;
int di[MAXN];

void pre()
{
    fill(di, di + MAXN, 1);

    nrep(i, 2, MAXN) {
        if (di[i] != 1) {
            continue;
        }

        for (int j = i; j < MAXN; j += i) {
            di[j] = i;
        }
    }
}

#define TEST 0

void solve()
{
    int n;
    cin >> n;

    vi a(n);
    cin >> a;

    int s, t;
    cin >> s >> t;
    s--, t--;

    if (s == t) {
        cout << "1\n";
        cout << s + 1 << '\n';
        return;
    }

    if (a[s] == 1 || a[t] == 1) {
        cout << "-1\n";
        return;
    }

    if (a[s] == a[t]) {
        cout << "2\n";
        cout << s + 1 << ' ' << t + 1 << '\n';
        return;
    }

    V<bool> used(3e5 + 1);
    used[a[s]] = true;
    used[a[t]] = true;

    vvi graph(MAXN + n);
    auto getgraph = [&](int i) {
        int now = a[i];
        while (now > 1) {
            int prev = di[now];
            while (di[now] == prev) {
                now /= di[now];
            }
            graph[prev].push_back(i + MAXN);
            graph[i + MAXN].push_back(prev);
        }
    };

    getgraph(s);
    getgraph(t);

    rep(i, n) {
        // if ((i != s && a[i] == a[s]) || (i != t && a[i] == a[t])) {
        //     continue;
        // }
        // pos[a[i]] = i;

        if (used[a[i]]) {
            continue;
        }

        used[a[i]] = true;
        getgraph(i);
    }

    // nrep(i, 2, 3e5 + 1) {
    //     if (pos[i] == -1) {
    //         continue;
    //     }
    //
    //     for (int j = i * 2; j <= 3e5; j += i) {
    //         if (pos[j] == -1) {
    //             continue;
    //         }
    //
    //         graph[pos[i]].push_back(pos[j]);
    //         graph[pos[j]].push_back(pos[i]);
    //     }
    // }

    vi dis(MAXN + n, oo);
    vi parent(MAXN + n, -1);
    queue<int> q;
    dis[s + MAXN] = 0;
    q.push(s + MAXN);

    while (!q.empty()) {
        auto i = q.front();
        q.pop();

        for (auto j : graph[i]) {
            if (dis[j] > dis[i] + 1) {
                dis[j] = dis[i] + 1;
                parent[j] = i;
                q.push(j);
            }
        }
    }

    if (dis[t + MAXN] == oo) {
        cout << "-1\n";
        return;
    }

    vi ans;
    int now = t + MAXN;
    while (parent[now] != -1) {
        if (now >= MAXN) {
            ans.push_back(now - MAXN + 1);
        }
        now = parent[now];
    }

    ans.push_back(s + 1);
    reverse(all(ans));
    cout << ans.size() << '\n';
    cout << ans;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(nullptr);

    pre();

    int t;
    (TEST && cin >> t) || (t = 1);
    while (t--) {
        solve();
    }
}