<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:
        len_nums = len(nums)
        prefix_div = [0] * len_nums
        ans = 10**9
        prefix_div[0] = nums[0] % p
        for i in range(1, len_nums):
            prefix_div[i] = (prefix_div[i-1] + nums[i]) % p

        if prefix_div[len_nums - 1] == 0:
            return 0 
        print(prefix_div)
        pos = {}
        pos[prefix_div[0]] = 0
        for i in range(1, len_nums):
            if prefix_div[i] == 0:
                ans = min(ans, len_nums - i- 1)
            if prefix_div[len_nums - 1] - prefix_div[i] == 0 and len_nums - 1 != i:
                ans = min(ans, i + 1)
            if (p - prefix_div[len_nums - 1] + prefix_div[i]) % p in pos:
                print(ans)
                ans = min(ans, i - pos[(p - prefix_div[len_nums - 1] + prefix_div[i]) % p])
            pos[prefix_div[i]] = i
        print(pos)
        if ans == 10 ** 9:
            return -1
        return ans
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