<p>Given an array of positive integers <code>nums</code>, remove the <strong>smallest</strong> subarray (possibly <strong>empty</strong>) such that the <strong>sum</strong> of the remaining elements is divisible by <code>p</code>. It is <strong>not</strong> allowed to remove the whole array.</p>

<p>Return <em>the length of the smallest subarray that you need to remove, or </em><code>-1</code><em> if it&#39;s impossible</em>.</p>

<p>A <strong>subarray</strong> is defined as a contiguous block of elements in the array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [3,1,4,2], p = 6
<strong>Output:</strong> 1
<strong>Explanation:</strong> The sum of the elements in nums is 10, which is not divisible by 6. We can remove the subarray [4], and the sum of the remaining elements is 6, which is divisible by 6.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [6,3,5,2], p = 9
<strong>Output:</strong> 2
<strong>Explanation:</strong> We cannot remove a single element to get a sum divisible by 9. The best way is to remove the subarray [5,2], leaving us with [6,3] with sum 9.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3], p = 3
<strong>Output:</strong> 0
<strong>Explanation:</strong> Here the sum is 6. which is already divisible by 3. Thus we do not need to remove anything.
</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>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>1 &lt;= p &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def minSubarray(self, nums: List[int], p: int) -> int:
        total_sum = sum(nums)
        target = total_sum % p
        
        # If the sum is already divisible by p, no need to remove any subarray
        if target == 0:
            return 0
        
        prefix_sum_mod = 0
        mod_map = {0: -1}  # To handle cases where the subarray starts from the beginning
        min_len = float('inf')
        
        for i, num in enumerate(nums):
            prefix_sum_mod = (prefix_sum_mod + num) % p
            required_mod = (prefix_sum_mod - target) % p
            
            # If the required mod exists in the map, calculate the subarray length
            if required_mod in mod_map:
                print(i, required_mod)
                min_len = min(min_len, i - mod_map[required_mod])
            
            # Store the current prefix sum mod in the map
            mod_map[prefix_sum_mod] = i
        
        # If we found a valid subarray, return its length, else return -1
        if min_len == float('inf') or min_len == len(nums):
            min_len = -1
        return min_len
422