<p>A binary watch has 4 LEDs on the top to represent the hours (0-11), and 6 LEDs on the bottom to represent&nbsp;the minutes (0-59). Each LED represents a zero or one, with the least significant bit on the right.</p>

<ul>
	<li>For example, the below binary watch reads <code>&quot;4:51&quot;</code>.</li>
</ul>

<p><img alt="" src="https://assets.leetcode.com/uploads/2021/04/08/binarywatch.jpg" style="width: 500px; height: 500px;" /></p>

<p>Given an integer <code>turnedOn</code> which represents the number of LEDs that are currently on (ignoring the PM), return <em>all possible times the watch could represent</em>. You may return the answer in <strong>any order</strong>.</p>

<p>The hour must not contain a leading zero.</p>

<ul>
	<li>For example, <code>&quot;01:00&quot;</code> is not valid. It should be <code>&quot;1:00&quot;</code>.</li>
</ul>

<p>The minute must&nbsp;consist of two digits and may contain a leading zero.</p>

<ul>
	<li>For example, <code>&quot;10:2&quot;</code> is not valid. It should be <code>&quot;10:02&quot;</code>.</li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> turnedOn = 1
<strong>Output:</strong> ["0:01","0:02","0:04","0:08","0:16","0:32","1:00","2:00","4:00","8:00"]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> turnedOn = 9
<strong>Output:</strong> []
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= turnedOn &lt;= 10</code></li>
</ul>

class Solution {
public:
    vector<int> hour = {1, 2, 4, 8};
    vector<int> minute = {1, 2, 4, 8, 16, 32};
    void solve(vector<string>& res, pair<int, int> time, int num, int start) {
        if(num == 0) {
            res.push_back(to_string(time.first) + (time.second < 10 ? ":0" : ":") + to_string(time.second));
        }
        for(int i=start; i < hour.size() + minute.size(); i++) {
            if(i < hour.size()) {
                time.first += hour[i];
                if(time.first < 12) {
                    solve(res, time, num-1, i + 1);
                } 
                time.first -= hour[i];
            } else {
                time.second += minute[i - hour.size()]; // modify minute
                if(time.second < 60) {
                    solve(res, time, num-1, i + 1);
                }
                time.second -= minute[i - hour.size()];
            }
        }
    }
    vector<string> readBinaryWatch(int turnedOn) {
        if(turnedOn > 8) {
            return vector<string>{};
        }
        vector<string> ans;
        solve(ans, make_pair(0, 0), turnedOn, 0);
        //sort(ans.begin(), ans.end());
        return ans;
    }
};
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