For any two positive integers $$$a$$$ and $$$b$$$, define the function by the following C++ code:

std::string gen_string(int64_t a, int64_t b) {
  std::string res;
  int64_t ia = 0, ib = 0;
  while (ia + ib < a + b) {
    if ((__int128)ia * b <= (__int128)ib * a) {
      res += '0';
      ia++;
    } else {
      res += '1';
      ib++;
    }
  }
  return res;
}

$$$ia$$$ will equal $$$a$$$ and $$$ib$$$ will equal $$$b$$$ when the loop terminates, so this function returns a bitstring of length $$$a+b$$$ with exactly $$$a$$$ zeroes and $$$b$$$ ones. For example, $$$gen\_string(4,10)=01110110111011$$$.

Given the argument of $$$A, B$$$, you should calculate the number of different subsequences of $$$gen\_string(A, B)$$$, and print it modulo $$$998244353$$$.

NOTE: A sequence $$$a$$$ is a subsequence of a string $$$b$$$ if $$$a$$$ can be obtained from b by deleting several (possibly, zero or all) elements.