<p>Find all valid combinations of <code>k</code> numbers that sum up to <code>n</code> such that the following conditions are true:</p>

<ul>
	<li>Only numbers <code>1</code> through <code>9</code> are used.</li>
	<li>Each number is used <strong>at most once</strong>.</li>
</ul>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> k = 3, n = 7
<strong>Output:</strong> [[1,2,4]]
<strong>Explanation:</strong>
1 + 2 + 4 = 7
There are no other valid combinations.</pre>

<p><strong class="example">Example 2:</strong></p>

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

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> k = 4, n = 1
<strong>Output:</strong> []
<strong>Explanation:</strong> 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 &gt; 1, there are no valid combination.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= k &lt;= 9</code></li>
	<li><code>1 &lt;= n &lt;= 60</code></li>
</ul>

class Solution {
public:

    void helper(vector<vector<int>>& res,vector<int> nums, int count,int n) {
        if (count<=0||nums.empty()) {return;}
        if (nums.back()>n) {return;}
        // exclude the last value in nums
        int last = nums.back();
        nums.pop_back();
        if (count==1 & last==n) {
            vector<int> v;
            v.push_back(last);
            res.push_back(v);
            return;
        }
        helper(res,nums,count,n);
        // include the last value in nums
        vector<vector<int>> res1;
        helper(res1,nums,count-1,n-last);
        if (!res1.empty()) {
            for (int i=0;i<res1.size();i++) {
                res1[i].push_back(last);
            }
            res.insert(res.end(),res1.begin(),res1.end());
        }
    }

    vector<vector<int>> combinationSum3(int k, int n) {
        vector<int> nums = {9,8,7,6,5,4,3,2,1};
        vector<vector<int>> res;
        helper(res,nums,k,n);
        return res;
    }
};
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