<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 {
private:
    void recsol(int k, int target, vector<int> nums, vector<vector<int>>& result, vector<int> combination, int s,int digits, int index){
        if(target==0 && digits==k){
            result.push_back(combination);
            return;
        }
        else{
            for(int i=index; i<s; i++){
                if(nums[i]<=target && digits<k){
                    combination.push_back(nums[i]);
                    target -= nums[i];
                    digits=digits + 1;
                    recsol(k, target, nums, result, combination, s, digits, i+1);
                    combination.pop_back();
                    digits= digits-1;
                    target += nums[i];

                }
                else{
                    return;
                }
            }
        }
    }
public:
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> result;
        vector<int> nums;
        for(int i=1; i<=9; i++){
            nums.push_back(i);
        }
        int digits=0;
        int s=nums.size();
        vector<int> combination;
        recsol(k, n, nums, result, combination, s, digits, 0);
        return result;
    }
};
9400