<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return <em>the length of the shortest non-empty <strong>subarray</strong> of </em><code>nums</code><em> with a sum of at least </em><code>k</code>. If there is no such <strong>subarray</strong>, return <code>-1</code>.</p>

<p>A <strong>subarray</strong> is a <strong>contiguous</strong> part of an array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> nums = [1], k = 1
<strong>Output:</strong> 1
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> nums = [1,2], k = 4
<strong>Output:</strong> -1
</pre><p><strong class="example">Example 3:</strong></p>
<pre><strong>Input:</strong> nums = [2,-1,2], k = 3
<strong>Output:</strong> 3
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>5</sup> &lt;= nums[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def shortestSubarray(self, nums: List[int], k: int) -> int:
        min_len = float("inf")
        queue = []  # (Prefix sum end idx) increasing monotonic queue.

        prefix_sums = []
        for idx, num in enumerate(nums):
            if num >= k:
                return 1

            if not prefix_sums:  # 1st int.
                prefix_sums.append(num)
                queue.append(idx)
                continue
            
            prefix_sums.append(prefix_sums[-1] + num)  # Update prefix sum at idx.

            # Subarrays from (queue[0] + 1)th idx to (idx)th idx.
            while queue and prefix_sums[-1] - prefix_sums[queue[0]] >= k:
                current_len = idx - queue.pop(0)
                if current_len < min_len:
                    min_len = current_len

            # Subarray from 0th idx to (idx)th idx.
            if prefix_sums[-1] >= k and idx + 1 < min_len:
                min_len = idx + 1

            # Make queue's stored prefix sums smaller as bigger subarray sum is preferred.
            while queue and prefix_sums[-1] < prefix_sums[queue[-1]]:
                queue.pop(-1)

            queue.append(idx)

        return min_len if min_len != float("inf") else -1

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