------
## 最终结论
```python
def can_convert_string(s, t, k):
    if len(s) != len(t):
        return False

    shifts_needed = [0] * 26

    for sc, tc in zip(s, t):
        shift = (ord(tc) - ord(sc)) % 26
        if shift > 0:
            shifts_needed[shift] += 1

    max_moves = 0
    for i in range(1, 26):
        max_moves = max(max_moves, (shifts_needed[i] - 1) * 26 + i)

    return max_moves <= k

# Example usage:
print(can_convert_string("input", "ouput", 9))  # Output: True
print(can_convert_string("abc", "bcd", 10))    # Output: False
print(can_convert_string("aab", "bbb", 27))    # Output: True
```