------
## 最终结论
```python
def find_kth_bit(n, k):
    def generate_binary_string(n):
        if n == 1:
            return "0"
        
        prev_string = "0"
        for i in range(2, n + 1):
            inverted = ''.join('1' if bit == '0' else '0' for bit in prev_string)
            reversed_inverted = inverted[::-1]
            prev_string = prev_string + "1" + reversed_inverted
        
        return prev_string
    
    Sn = generate_binary_string(n)
    return Sn[k - 1]

# Example usage:
# print(find_kth_bit(3, 1))  # Output: "0"
# print(find_kth_bit(4, 11)) # Output: "1"
```