uint32_t mul_mod(uint32_t a, uint32_t b, uint32_t m) {
  uint32_t result = 0;
  uint32_t x = b % m;

  for (int i = 0; i < 32; ++i) {
    uint32_t myBit = 31 - i;
    //~ Serial.print(i);
    //~ Serial.print(": ");
    //~ Serial.println(((a << myBit) >> 31));
    if (((a << myBit) >> 31) == 1) {
      result = (result + x) % m;
    }
    x = (x << 1) % m;
  }

  return result;
}

uint32_t pow_mod(uint32_t base, uint32_t power, uint32_t m) {
  uint32_t result = 1;
  uint32_t x = base % m;
  for (int i = 0; i < 32; ++i ) {
    if ((power & (1UL << i)) != 0) {
      result = mul_mod(result, x, m);
    }
    x = mul_mod(x, x, m);
  }
  return result;
}