<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>

from collections import deque
from typing import List

class Solution:
    def shortestSubarray(self, nums: List[int], k: int) -> int:
        n = len(nums)
        prefix_sum = [0] * (n + 1)
        
        # Compute the prefix sums
        for i in range(n):
            prefix_sum[i + 1] = prefix_sum[i] + nums[i]
        
        # Deque to store the indices of the prefix sums
        deq = deque()
        min_length = float('inf')
        
        for i in range(n + 1):
            # Remove indices from the deque where the prefix sum is no longer useful
            while deq and prefix_sum[i] - prefix_sum[deq[0]] >= k:
                min_length = min(min_length, i - deq.popleft())
            
            # Maintain the deque to have increasing prefix sums
            while deq and prefix_sum[i] <= prefix_sum[deq[-1]]:
                deq.pop()
            
            deq.append(i)
        
        return min_length if min_length != float('inf') else -1
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