<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 {
private:
    vector<int> hours = {1, 2, 4, 8};
    vector<int> minutes = {1, 2, 4, 8, 16, 32};

    void backTrack(int start, int num, pair<int, int> time, vector<string>& ans){
        if(num == 0){
            ans.push_back(to_string(time.first) + (time.second < 10 ? ":0" : ":") + to_string(time.second));
            return;
        }

        for(int i = start; i < hours.size() + minutes.size(); i++){
            if( i < hours.size()){
                time.first += hours[i];
                if(time.first < 12) backTrack(i + 1, num - 1, time, ans);
                time.first -= hours[i];
            }else{
                time.second += minutes[i - hours.size()];
                if(time.second < 60) backTrack(i + 1, num - 1, time, ans);
                time.second -= minutes[i - hours.size()];
            }
        }
    }

public:
    vector<string> readBinaryWatch(int turnedOn) {
        vector<string> ans;
        backTrack(0, turnedOn, make_pair(0, 0), ans);
        return ans;
    }
};
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