<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:
    int findCombo(int kp, map <string, string> &m ,int k, int n, vector<vector<int>> &res, int sum, int start, int *idx, string s, int *len) {
        int ret = -1;
        if (s != "" && m[s].length() != 0) {
            start = (m[s][m[s].length() -1] - '0') + 1;
        }
        if (start == 10) {
            return -1;
            *len = *len - 1;
        }

        for (int i = start; i < 10; i++) {
            sum += i;
            if (k == 1) {
                if (sum == n) {
                    res.push_back({i});
                    // searched[kp - k] += ('0' + i);
                    return i;
                } else {
                    // continue;
                }
            } else {
                s += ('0' + i);
                int result = findCombo(kp, m, k-1, n, res, sum, i + 1, idx, s, len);
                if (result != -1) {
                    res[*idx].push_back(i);
                    if (s.length() == *len) {
                        m[s] += ('0' + result);
                    }
                    
                    return i;
                }
                s.pop_back();
            }
                
                
            sum -= i;
        }

        return ret;
    }


   
    vector<vector<int>> combinationSum3(int k, int n) {
        vector<vector<int>> res;
        int sum = 0;
        int idx = 0;
        vector<string> s (k, "");
        map <string, string> m;
        int len = k - 1;

        // for (int i = 1; i < 10; i++) {
            // findCombo(k, s, k, n, res, sum,  1, &idx);
           while ( findCombo(k, m, k, n, res, sum,  1, &idx, "", &len) != -1 ) {
                idx++;
           }

        // }
            

        return res;
        
    }
};
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