------
## 最终结论
```python
def zigzag(n, k):
    if k == 0:
        return 1
    if n == 0 or k > n:
        return 0
    return zigzag(n, k - 1) + zigzag(n - 1, n - k)

# Test cases
assert zigzag(4, 3) == 5
assert zigzag(4, 2) == 4
assert zigzag(3, 1) == 1
```