<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<string> readBinaryWatch(int turnedOn) {
    vector<string> ans;
    dfs(turnedOn, 0, 0, 0, ans);
    return ans;
  }

 private:
  static constexpr int hours[4] = {1, 2, 4, 8};
  static constexpr int minutes[6] = {1, 2, 4, 8, 16, 32};

  void dfs(int turnedOn, int s, int h, int m, vector<string>& ans) {
    if (turnedOn == 0) {
      string time = to_string(h) + ":" + (m < 10 ? "0" : "") + to_string(m);
      ans.push_back(time);
      return;
    }

    for (int i = s; i < 4 + 6; ++i)
      if (i < 4 && h + hours[i] < 12)
        dfs(turnedOn - 1, i + 1, h + hours[i], m, ans);
      else if (i >= 4 && m + minutes[i - 4] < 60)
        dfs(turnedOn - 1, i + 1, h, m + minutes[i - 4], ans);
  }
};
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