// Problem Forge, Problem of the Month, rungs 06 and 07: the rule.  CC0 1.0 (public domain).
// Vertices i < j are joined when the first bit of SHA-256(K, i, j) is 1,
// with K as its 32 bytes and i, j as 8-byte big-endian numbers.
// Build: c++ -std=c++17 rule.cpp -lcrypto      Use: ./a.out KEY i j   (prints 1 if joined, else 0)
#include <openssl/sha.h>
#include <array>
#include <cstdint>
#include <iostream>
#include <string>
#include <utility>

bool joined(const std::array<unsigned char, 32> & key, std::uint64_t i, std::uint64_t j) {
   if (i > j) {
      std::swap(i, j);
   }
   unsigned char msg[48], out[32];
   for (int b = 0; b < 32; ++b) {
      msg[b] = key[b];
   }
   for (int b = 0; b < 8; ++b) {
      msg[32 + b] = static_cast<unsigned char>(i >> (56 - 8 * b));
      msg[40 + b] = static_cast<unsigned char>(j >> (56 - 8 * b));
   }
   SHA256(msg, sizeof msg, out);
   return out[0] & 0x80;
}

int main(int argc, char ** argv) {
   if (argc != 4) {
      return 2;
   }
   std::array<unsigned char, 32> key{};
   for (int b = 0; b < 32; ++b) {
      key[b] = static_cast<unsigned char>(std::stoi(std::string(argv[1] + 2 * b, 2), nullptr, 16));
   }
   std::cout << joined(key, std::stoull(argv[2]), std::stoull(argv[3])) << "\n";
}