AntiHash

#include <iostream>
#include <vector>
#include <algorithm>
#include <string>

using namespace std;


struct Number {
  long long value;
  vector<int> add;
  vector<int> sub;
};

bool operator<(Number n1, Number n2) {
  return n1.value < n2.value;
}

Number sub(Number n1, const Number& n2, long long m) {
  n1.value = ((n1.value - n2.value) % m + m) % m;
  copy(n2.add.begin(), n2.add.end(), back_inserter(n1.sub));
  copy(n2.sub.begin(), n2.sub.end(), back_inserter(n1.add));
  return n1;
}

long long h(string s, long long p, long long m) {
  long long h = 0;
  long long q = 1;
  for (int i = 0; i < s.size(); ++i) {
    h = (h + s[i] * q) % m;
    q = (p * q) % m;
  }
  return h;
}

bool solve(long long p, long long m, int n) {
  long long q = 1;
  vector<Number> numbers(n);
  for (int i = 0; i < n; ++i) {
    numbers[i].value = q;
    numbers[i].add.push_back(i);
    q = (q * p) % m;
  }


  while (numbers.size() > 1) {
    sort(numbers.begin(), numbers.end());
    if (numbers[0].value == 0) break;
    for (int i = 0; i < numbers.size() / 2; ++i) {
      Number& n1 = numbers[2 * i + 0];
      Number& n2 = numbers[2 * i + 1];
      numbers[i] = sub(n2, n1, m);
    }
    numbers.resize(numbers.size() / 2);
  }
  if (numbers[0].value != 0) {
    return false;
  }
  string s1 = "";
  string s2 = "";
  for (int i = 0; i < n; ++i) {
    s1 += 'a';
    s2 += 'a';
  }
  for (int i : numbers[0].add) s1[i]++;
  for (int i : numbers[0].sub) s2[i]++;
  cout << s1 << endl;
  cout << s2 << endl;
  cout << h(s1, p, m) << endl;
  cout << h(s2, p, m) << endl;
  return true;
}

int main() {
  for (int n = 1; n <= 1000; ++n) {
    if (solve(31, 1000000007, n)) {
      break;
    }
  }
  return 0;
}