<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:
        cums = [0]
        for i, num in enumerate(nums):
            cums.append(num + cums[-1])
        min_length = math.inf
        stack_val = []
        stack_idx = []
        for i in range(len(cums)):
            while stack_val and cums[i] <= stack_val[-1]:
                stack_val.pop()
                stack_idx.pop()
            
            if stack_val:
                low, high = 0, len(stack_val)-1
                while low < high - 1:
                    mid = int((low + high) // 2)
                    if cums[i] - stack_val[mid] >= k:
                        low = mid
                    else:
                        high = mid
                if cums[i] - stack_val[high] >= k:
                    min_length = min(min_length, i - stack_idx[high])
                elif cums[i] - stack_val[low] >= k:
                    min_length = min(min_length, i - stack_idx[low])
                
            stack_val.append(cums[i])
            stack_idx.append(i)

        return -1 if min_length == math.inf else min_length




# class Solution:
#     def shortestSubarray(self, nums: List[int], k: int) -> int:
#         cums = [0]
#         for i, num in enumerate(nums):
#             cums.append(num + cums[-1])
#         min_length = math.inf
#         stack_val = []
#         stack_idx = []
#         for i in range(len(cums)):
#             while stack_val and cums[i] <= stack_val[-1]:
#                 stack_val.pop()
#                 stack_idx.pop()
#             for j in range(len(stack_val)-1,-1,-1):
#                 if i - stack_idx[j] >= min_length:
#                     break
#                 if cums[i] - stack_val[j] >= k:
#                     min_length = min(min_length, i - stack_idx[j])
#                     break
#             stack_val.append(cums[i])
#             stack_idx.append(i)

#         return -1 if min_length == math.inf else min_length



# class Solution:
#     def shortestSubarray(self, nums: List[int], k: int) -> int:
#         cums = [0]
#         for num in nums:
#             cums.append(num + cums[-1])
#         print(cums)
#         cnt = defaultdict(int)
#         min_length = math.inf
#         for i,cum in enumerate(cums):
#             print(cum,cnt)
#             if cum > 0:
#                 for key,val in cnt.items():
#                     if cum - k >= key:
#                         print(i-val)
#                         min_length = min(min_length, i-val)
#             cnt[cum] = i

#         return -1 if min_length == math.inf else min_length


# class Solution:
#     def shortestSubarray(self, nums: List[int], k: int) -> int:
#         n = len(nums)
#         shortest = math.inf
#         current_sum = 0
#         left, right = 0, 0
#         stack_i = []
#         stack_sum = []
#         while right < n:
#             if current_sum < k:
#                 if nums[right] >= 0:
#                     current_sum += nums[right]
#                     stack_i.append(right)
#                     stack_sum.append(current_sum)
#                     right += 1
#                 else:
#                     if nums[right] + current_sum <= 0:
#                         current_sum = 0
#                         left = right + 1
#                         right += 1
#                         stack_i = []
#                         stack_sum = []
#                     else:
#                         current_sum += nums[right]
#                         while stack_sum and current_sum < stack_sum[-1]:
#                             stack_i.pop(-1)
#                             stack_sum.pop(-1)
#                         stack_i.append(right)
#                         stack_sum.append(current_sum)
#                         right += 1
#             if current_sum >= k:
#                 # print(f'current_sum: {current_sum}')
#                 # print(f'stack_i: {stack_i}')
#                 # print(f'stack_sum: {stack_sum}')
#                 # print(f'left: {left}')
#                 # print(f'right: {right}')


#                 # binary search
#                 target_i = left-1
#                 if stack_sum:
#                     low = 0
#                     high = len(stack_sum)-1
#                     while low < high - 1:
#                         mid = int((low+high) // 2)
#                         if current_sum - stack_sum[mid] >= k:
#                             low = mid
#                         else:
#                             high = mid
#                     if current_sum - stack_sum[high] >= k:
#                         target_i = stack_i[high]
#                         stack_i = stack_i[high+1:]
#                         stack_sum = stack_sum[high+1:]
#                     elif current_sum - stack_sum[low] >= k:
#                         target_i = stack_i[low]
#                         stack_i = stack_i[low+1:]
#                         stack_sum = stack_sum[low+1:]
#                     else:
#                         target_i = left-1

#                 shortest = min(shortest, right-1-target_i)
#                 target_i = stack_i.pop(0)
#                 target_sum = stack_sum.pop(0)
#                 left = target_i + 1
#                 current_sum -= target_sum
#                 stack_sum = [v-target_sum for v in stack_sum]

#         return -1 if shortest == math.inf else shortest
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