<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 func(vector<vector<int>>& l,int k,int n,vector<int> v,vector<bool> b,int ind,int sum){
        cout<<k<<" "<<n<<" "<<ind<<" "<<sum<<endl;
        if(ind==k){
            if(sum==n){
                l.push_back(v);
            }
            return;
        }
        for(int i=1;i<=9;i++){
            if(!b[i-1]){
                if(ind>0){
                    if(i<=v[ind-1]){
                        continue;
                    }
                }
                v.push_back(i);
                b[i-1]=true;
                func(l,k,n,v,b,ind+1,sum+i);
                b[i-1]=false;
                v.erase(v.end());
            }
        }
    }
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> l;
        func(l,k,n,vector<int> {},vector<bool> (9,false),0,0);
        return l;
    }
};
10600