C++ check if two sequences are equal using a 3rd sequence as criteria

I need to check if two given sequences are equal, but if I find a mismatched element I need to check in a 3rd sequence (same size of the other two) if that can be ignored.

I know that I can write a simple algorithm to solve that, but I would like to know if there is any C++-like style to solving this, using a std algorithm.

Example:

A = [1, 2, 3, 4, 5, 6]
B = [1, 2, 3, A, 5, 6]
M = [true, true, true, false, true, true]
N = [true, true, true, true, true, true]

bool equal1 = the_equal(begin_A, end_A, begin_B, begin_M); // Should return true, even if '4' is different from 'A' since in the same position of the found mismatch, in the M sequence, we have a false that indicates that position should be ignored.

bool equal2 = the_equal(begin_A, end_A, begin_B, begin_N); // Should return false, since '4' is different from 'A' and we have a true in sequence N for that position.

That could be solved by something like:

template<I1, I2, I3> // iterators
bool the_equal(I1 first1, I1 last1, I2 first2, I3 first3) {
  while (first1 != last1) {
    if (first1 != first2 && first3 != false)
      return false;
    ++first1; ++first2; ++first3;
  }

  return true;
}