<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>

#include <vector>
#include <set>
#include <algorithm>
#include <climits>

using namespace std;

class Solution {
public:
    vector<int> smallestRange(vector<vector<int>>& nums) {
        set<int> s;
        for (const auto& row : nums) {
            for (int num : row) {
                s.insert(num);
            }
        }

        int x = 0, y = INT_MAX;
        for (int i : s) {
            int lo = 0;
            int hi = *s.rbegin() - *s.begin();
            while (lo < hi) {
                int mid = (lo + hi) >> 1;
                bool valid = true;
                for (const auto& row : nums) {
                    auto left = lower_bound(row.begin(), row.end(), i);
                    auto right = upper_bound(row.begin(), row.end(), i + mid);
                    if (right == left) {
                        valid = false;
                        lo = mid + 1;
                        break;
                    }
                }
                if (valid) {
                    hi = mid;
                }
            }
            if (lo < y - x || (lo == y - x && i < x)) {
                x = i;
                y = i + lo;
            }
        }

        return {x, y};
    }
};

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