#include <stdio.h>
#include <vector>
#include <string>
 
int main() {
  std::vector<int> s = {2, 2};
  for (; s.size() != 1;) {
    for (auto i = 0ul; i < s.size() - 1; i++) {
      printf("ack(%d, ", s[i]);
    }
    printf("%d%s\n", s.back(), std::string(s.size() - 1, ')').c_str());
    auto m = s[s.size() - 2], n = s[s.size() - 1];
    if (m == 0) {
      s.pop_back();
      s.back() = n + 1;
    } else if (n == 0) {
      s[s.size() - 2] = m - 1;
      s[s.size() - 1] = 1;
    } else {
      s[s.size() - 2] = m - 1;
      s[s.size() - 1] = m;
      s.push_back(n - 1);
    }
  }
  printf("%d\n", s.back());
  return 0;
}

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