Write a Python function `min_k` that takes a list of tuples and an integer `K` as input. Each tuple contains a string and an integer. The function should return the `K` tuples with the smallest integer values, sorted in ascending order of these values.
#### Example Usage
```python [main.nopy]
# Example 1
input_list = [('Manjeet', 10), ('Akshat', 4), ('Akash', 2), ('Nikhil', 8)]
K = 2
print(min_k(input_list, K)) # Output: [('Akash', 2), ('Akshat', 4)]
# Example 2
input_list = [('Sanjeev', 11), ('Angat', 5), ('Akash', 3), ('Nepin', 9)]
K = 3
print(min_k(input_list, K)) # Output: [('Akash', 3), ('Angat', 5), ('Nepin', 9)]
# Example 3
input_list = [('tanmay', 14), ('Amer', 11), ('Ayesha', 9), ('SKD', 16)]
K = 1
print(min_k(input_list, K)) # Output: [('Ayesha', 9)]
```
#### Constraints
- The input list will contain at least `K` tuples.
- The integer values in the tuples are unique.
- The function should return a new list and not modify the input list.