<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: List[List[int]]) -> List[int]:
        
        q = []
        l, r = float('inf'), -float('inf')
        for idx, sub in enumerate(nums):
            q.append((sub[0], idx, 0))
            if sub[0] < l:
                l = sub[0]
            if sub[0] > r:
                r = sub[0]

        seg = [(l, r)] 
        heapq.heapify(q)

        while q:
            cur, idx, idy = heapq.heappop(q)
            if idy+1 < len(nums[idx]):
               heapq.heappush(q, (nums[idx][idy+1], idx, idy+1))
               seg.append((q[0][0], max(seg[-1][1], nums[idx][idy+1])))
            else:
                break
        
        output, minv = [], float('inf')
        for sub in seg:
            if sub[1]-sub[0] < minv:
                minv = sub[1]-sub[0]
                output = [sub[0], sub[1]]
        return output
            

            

        
23700