# GeetCode Hub

Find all valid combinations of `k` numbers that sum up to `n` such that the following conditions are true:

• Only numbers `1` through `9` are used.
• Each number is used at most once.

Return a list of all possible valid combinations. The list must not contain the same combination twice, and the combinations may be returned in any order.

Example 1:

```Input: k = 3, n = 7
Output: [[1,2,4]]
Explanation:
1 + 2 + 4 = 7
There are no other valid combinations.```

Example 2:

```Input: k = 3, n = 9
Output: [[1,2,6],[1,3,5],[2,3,4]]
Explanation:
1 + 2 + 6 = 9
1 + 3 + 5 = 9
2 + 3 + 4 = 9
There are no other valid combinations.
```

Example 3:

```Input: k = 4, n = 1
Output: []
Explanation: There are no valid combinations.
Using 4 different numbers in the range [1,9], the smallest sum we can get is 1+2+3+4 = 10 and since 10 > 1, there are no valid combination.
```

Example 4:

```Input: k = 3, n = 2
Output: []
Explanation: There are no valid combinations.
```

Example 5:

```Input: k = 9, n = 45
Output: [[1,2,3,4,5,6,7,8,9]]
Explanation:
1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 = 45
There are no other valid combinations.
```

Constraints:

• `2 <= k <= 9`
• `1 <= n <= 60`

class Solution { public List<List<Integer>> combinationSum3(int k, int n) { } }