<p>Given two integers <code>n</code> and <code>k</code>, return <em>all possible combinations of</em> <code>k</code> <em>numbers chosen from the range</em> <code>[1, n]</code>.</p>

<p>You may return the answer in <strong>any order</strong>.</p>

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

<pre>
<strong>Input:</strong> n = 4, k = 2
<strong>Output:</strong> [[1,2],[1,3],[1,4],[2,3],[2,4],[3,4]]
<strong>Explanation:</strong> There are 4 choose 2 = 6 total combinations.
Note that combinations are unordered, i.e., [1,2] and [2,1] are considered to be the same combination.
</pre>

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

<pre>
<strong>Input:</strong> n = 1, k = 1
<strong>Output:</strong> [[1]]
<strong>Explanation:</strong> There is 1 choose 1 = 1 total combination.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 20</code></li>
	<li><code>1 &lt;= k &lt;= n</code></li>
</ul>

class Solution {
public:
    vector<vector<int>> combine(int n, int k) {
        if (computed[n][k]) {
            return result[n][k];
        }
        if (k > n) {
            return save_result(n, k, {});
        }
        if(k == 0 && n == 0) {
            return save_result(n, k, {{}});
        }
        if(k == 0) {
            return save_result(n, k, {{}});
        }
        auto not_included_v = combine(n - 1, k);
        auto included_v = combine(n - 1, k - 1);
        for(auto &v : included_v) 
        {
            v.push_back(n);
        }
        for(auto &x : not_included_v) {
            included_v.push_back(std::move(x));
        }
        return save_result(n, k, std::move(included_v));
    }
private:
    vector<vector<int>>& save_result(int n, int k, vector<vector<int>>&& part_result) {
        computed[n][k] = true;
        result[n][k] = std::move(part_result);
        return result[n][k];
    }
    static constexpr int N = 27;
    static constexpr int K = 27;
    bool computed[N][K] = { };
    vector <vector<int>> result[N][K] = { };
};
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