<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:
    map<pair<int,int>,vector<vector<int>>> M;
    vector<vector<int>> calc(int n,int k){
        if(M.find({n,k}) != M.end()){
            return M[{n,k}];
        }
        vector<vector<int>> result1 = calc(n-1,k);
        vector<vector<int>> result2 = calc(n-1,k-1);
        for(int i=0;i<result2.size();i++){
            result2[i].push_back(n);
        }
        result1.insert(result1.end(),result2.begin(),result2.end());
        M[{n,k}] = result1;
        return result1;
    }
    vector<vector<int>> combine(int n, int k) {
        vector<vector<int>> result;
        for(int i=1;i<=n;i++){
            result.push_back({i});
            M[{i,1}] = result;
        }
        result = {{}};
        for(int i=1;i<=k;i++){
            result[0].push_back(i);
            M[{i,i}] = result;
        }
        return calc(n,k);
    }
};

// calculate i choose i for each i.(for first k elements)
//
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