<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:
    def readBinaryWatch(self, turnedOn: int) -> List[str]:
        self.data = [0] * 10
        return list(self.visit(0, turnedOn))
    
    def visit(self, d, r):
        if d == 10:
            if r == 0:
                x = self.data
                hour = sum(x[i] << i for i in range(4))
                minute = sum(x[i+4] << i for i in range(6))
                if hour < 12 and minute < 60:
                    yield f'{hour}:{minute:02}'
            return
        yield from self.visit(d+1, r)
        if r > 0:
            self.data[d] = 1
            yield from self.visit(d+1, r-1)
            self.data[d] = 0
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