<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

class Solution:
    def shortestSubarray(self, nums, k):
        n = len(nums)
        prefix_sum = [0] * (n + 1)
        for i in range(n):
            prefix_sum[i + 1] = prefix_sum[i] + nums[i]
        
        result = n + 1
        deq = deque()
        
        for i in range(n + 1):
            # Remove any index from the front of the deque 
            # if the sum prefix_sum[i] - prefix_sum[index] >= k
            while deq and prefix_sum[i] - prefix_sum[deq[0]] >= k:
                result = min(result, i - deq.popleft())
            
            # Remove any index from the back of the deque 
            # if prefix_sum[i] <= prefix_sum[index] to 
            # maintain the increasing order of prefix sums
            while deq and prefix_sum[i] <= prefix_sum[deq[-1]]:
                deq.pop()
            
            # Append the current index to the deque
            deq.append(i)
        
        return result if result <= n else -1

# Example usage:
solution = Solution()
nums = [2, -1, 2]
k = 3
print(solution.shortestSubarray(nums, k))  # Output: 3
31800