<p>You have <code>k</code> lists of sorted integers in <strong>non-decreasing&nbsp;order</strong>. Find the <b>smallest</b> range that includes at least one number from each of the <code>k</code> lists.</p>

<p>We define the range <code>[a, b]</code> is smaller than range <code>[c, d]</code> if <code>b - a &lt; d - c</code> <strong>or</strong> <code>a &lt; c</code> if <code>b - a == d - c</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [[4,10,15,24,26],[0,9,12,20],[5,18,22,30]]
<strong>Output:</strong> [20,24]
<strong>Explanation: </strong>
List 1: [4, 10, 15, 24,26], 24 is in range [20,24].
List 2: [0, 9, 12, 20], 20 is in range [20,24].
List 3: [5, 18, 22, 30], 22 is in range [20,24].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [[1,2,3],[1,2,3],[1,2,3]]
<strong>Output:</strong> [1,1]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>nums.length == k</code></li>
	<li><code>1 &lt;= k &lt;= 3500</code></li>
	<li><code>1 &lt;= nums[i].length &lt;= 50</code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i][j] &lt;= 10<sup>5</sup></code></li>
	<li><code>nums[i]</code>&nbsp;is sorted in <strong>non-decreasing</strong> order.</li>
</ul>

class Solution:
    def smallestRange(self, nums):
        min_x = 0
        min_y = inf
        max_value = -inf
        next_indices = [0] * len(nums)
        
        # Min-heap using tuples (value, list_index)
        min_queue = []

        # Initialize the heap with the first element from each list
        for i in range(len(nums)):
            heappush(min_queue, (nums[i][0], i))
            max_value = max(max_value, nums[i][0])

        flag = True
        while flag:
            min_val, min_list_index = heappop(min_queue)
            
            # Update the range if better
            if min_y - min_x > max_value - min_val:
                min_x = min_val
                min_y = max_value

            # Move to the next element in the selected list
            next_indices[min_list_index] += 1
            if next_indices[min_list_index] == len(nums[min_list_index]):
                # If we've used all elements from one list, we cannot continue the search
                break
            
            # Get the next element from this list
            next_val = nums[min_list_index][next_indices[min_list_index]]
            heappush(min_queue, (next_val, min_list_index))
            max_value = max(max_value, next_val)

        return [min_x, min_y]

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