p411.ans1
======================
aca


=================
p411.ans2
======================
abba


=================
p411.cpp
======================
#include <bits/stdc++.h>
// #include <coding_library/strings/hashing.hpp>

using namespace std;

template<typename T1, typename T2>
ostream& operator<<(ostream& out, const pair<T1, T2>& x) {
    return out << x.first << ' ' << x.second;
}

template<typename T1, typename T2>
istream& operator>>(istream& in, pair<T1, T2>& x) {
    return in >> x.first >> x.second;
}

template<typename T>
istream& operator>>(istream& in, vector<T>& a) {
    for(auto& x: a) {
        in >> x;
    }
    return in;
};

template<typename T>
ostream& operator<<(ostream& out, const vector<T>& a) {
    for(auto x: a) {
        out << x << ' ';
    }
    return out;
};

class HashMeta {
  private:
    void set_random_base() {
        seed_seq seed{
            (uint32_t)chrono::duration_cast<chrono::nanoseconds>(
                chrono::high_resolution_clock::now().time_since_epoch()
            )
                .count(),
            (uint32_t)random_device()(), (uint32_t)42
        };
        mt19937 rng(seed);
        base = uniform_int_distribution<uint64_t>(0, mod - 1)(rng);
    }

    void precompute_base_pow(size_t n) {
        base_pow.resize(n);
        base_pow[0] = 1;
        for(size_t i = 1; i < n; i++) {
            base_pow[i] = mul(base_pow[i - 1], base);
        }
    }

    static constexpr uint64_t add(uint64_t a, uint64_t b) {
        a += b + 1;
        a = (a & mod) + (a >> 61);
        return a - 1;
    }

    static constexpr uint64_t sub(uint64_t a, uint64_t b) {
        return add(a, mod - b);
    }

    static constexpr uint64_t mul(uint64_t a, uint64_t b) {
        uint64_t l1 = (uint32_t)a, h1 = a >> 32, l2 = (uint32_t)b, h2 = b >> 32;
        uint64_t l = l1 * l2, m = l1 * h2 + l2 * h1, h = h1 * h2;
        uint64_t ret =
            (l & mod) + (l >> 61) + (h << 3) + (m >> 29) + (m << 35 >> 3) + 1;
        ret = (ret & mod) + (ret >> 61);
        ret = (ret & mod) + (ret >> 61);
        return ret - 1;
    }

  public:
    class hash_t {
        uint64_t h;

      public:
        hash_t() : h(0) {}
        hash_t(uint64_t h) : h(h) {}
        operator uint64_t() const { return h; }

        hash_t& operator+=(const hash_t& other) {
            h = add(h, other.h);
            return *this;
        }

        hash_t& operator-=(const hash_t& other) {
            h = sub(h, other.h);
            return *this;
        }

        hash_t& operator*=(const hash_t& other) {
            h = mul(h, other.h);
            return *this;
        }

        hash_t operator+(const hash_t& other) const {
            return hash_t(*this) += other;
        }
        hash_t operator-(const hash_t& other) const {
            return hash_t(*this) -= other;
        }
        hash_t operator*(const hash_t& other) const {
            return hash_t(*this) *= other;
        }

        bool operator==(const hash_t& other) const { return h == other.h; }
        bool operator!=(const hash_t& other) const { return h != other.h; }

        // For use in std::map and std::set
        bool operator<(const hash_t& other) const { return h < other.h; }
    };

    uint64_t base;
    vector<hash_t> base_pow;
    static constexpr uint64_t mod = (1ull << 61) - 1;

    void init(size_t n) {
        set_random_base();
        precompute_base_pow(n);
    }

    template<typename T>
    vector<hash_t> rabin_karp(const T& container) {
        vector<hash_t> h(container.size());
        for(size_t i = 0; i < container.size(); i++) {
            h[i] = (i ? h[i - 1] : hash_t(0)) * hash_t(base) +
                   hash_t(container[i]);
        }
        return h;
    }

    hash_t hash_range(int l, int r, const vector<hash_t>& h) {
        if(l == 0) {
            return h[r];
        }
        return h[r] - h[l - 1] * base_pow[r - l + 1];
    }
};

HashMeta hash_meta;
using hash_t = HashMeta::hash_t;

string a, b;

void read() { cin >> a >> b; }

vector<hash_t> ha, ha_rev, hb;

pair<int, int> check(int len) {
    map<hash_t, pair<int, int>> vis;

    for(int i = len - 1; i < (int)a.size(); i++) {
        int l = i - len + 1, r = i;
        int rev_l = (int)a.size() - r - 1;
        int rev_r = (int)a.size() - l - 1;

        hash_t fh = hash_meta.hash_range(l, r, ha);
        hash_t rh = hash_meta.hash_range(rev_l, rev_r, ha_rev);
        if(fh == rh) {
            vis[fh] = {l, r};
        }
    }

    for(int i = len - 1; i < (int)b.size(); i++) {
        hash_t fh = hash_meta.hash_range(i - len + 1, i, hb);
        auto it = vis.find(fh);

        if(it != vis.end()) {
            return it->second;
        }
    }

    return {-1, -1};
}

void solve() {
    // We can solve this with binary search and hashing. We need to consider two
    // cases - odd and even length of the palindrome and do two separate binary
    // searches, because the maximal odd length might be quite different from
    // the maximal even. The complexity will be O(S log^2 S). To check for a
    // given length, we will do backward and forward hash to identify the
    // palindromes in A of length L, then mark them in a map or as set (this is
    // the second log), and go through the substrings of length L in B, checking
    // if they appear in the map.

    hash_meta.init(a.size() + b.size());

    ha = hash_meta.rabin_karp(a);
    ha_rev = hash_meta.rabin_karp(string(a.rbegin(), a.rend()));
    hb = hash_meta.rabin_karp(b);

    pair<int, int> ans = {-1, -1};

    int low = 1, high = min(a.size(), b.size());
    while(low <= high) {
        int mid = (low + high) / 2;
        int len = 2 * mid - 1;
        auto res = check(len);
        if(res.first != -1) {
            if(ans.first == -1 ||
               res.second - res.first + 1 > ans.second - ans.first + 1) {
                ans = res;
            }
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }

    low = 1, high = min(a.size(), b.size());
    while(low <= high) {
        int mid = (low + high) / 2;
        int len = 2 * mid;
        auto res = check(len);
        if(res.first != -1) {
            if(ans.first == -1 ||
               res.second - res.first + 1 > ans.second - ans.first + 1) {
                ans = res;
            }
            low = mid + 1;
        } else {
            high = mid - 1;
        }
    }

    assert(ans.first != -1);
    cout << a.substr(ans.first, ans.second - ans.first + 1) << '\n';
}

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

    int T = 1;
    // cin >> T;
    for(int test = 1; test <= T; test++) {
        read();
        // cout << "Case #" << test << ": ";
        solve();
    }

    return 0;
}

=================
p411.in1
======================
abacaba
abracab

=================
p411.in2
======================
abbab
babbab

=================
statement.txt
======================
411. Petya the Hero
Time limit per test: 0.25 second(s)
Memory limit: 65536 kilobytes
input: standard
output: standard

Petya has come back from the Berland-Birland War, and now he is fond of gathering his friends and narrating his heroic deeds. You have probably heard the story telling that Petya, being isolated, captured two Birland officers single-handed, than, using their clothes and having got to know the password, penetrated into the army base of the enemy, forced the controlling system out of action and helped Berland army to seize the base. This story was also heard by Colonel Kruglyakovsky, who was especially interested in a detail. That is the way Petya managed to find out the password for entering the army base with his poor knowledge of Birland language. Called by the colonel young hero explained, that although Birland speech wasn't clear to him, it wasn't too difficult to write it down. At first Petya interrogated the captives and wrote down the speech of each one as a string of latin letters. He knew that Birland valid passwords could be read the same way in either direction, i.e. they were palindromes. So he had to use the program, searching for the longest common substring of two strings, which was valid as a password. After hearing the answer, Colonel Kruglyakovsky declared, that this program could be very useful for interrogation captives and for decoding secret messages... As far as Petya certanly hadn't any program, he asked you for help.
Input
The input file contains two non-empty strings that consist of lowercase latin letters ('a'-'z'). The length of each string doesn't exceed 2000 symbols. The strings contain at least one common letter.
Output
Output the password obtained by the program Petya has described. If there are several possible passwords, output any of them.
Example(s)
sample input
sample output
abacaba
abracab
aca

sample input
sample output
abbab
babbab
abba

=================
