<p>A split of an integer array is <strong>good</strong> if:</p>

<ul>
	<li>The array is split into three <strong>non-empty</strong> contiguous subarrays - named <code>left</code>, <code>mid</code>, <code>right</code> respectively from left to right.</li>
	<li>The sum of the elements in <code>left</code> is less than or equal to the sum of the elements in <code>mid</code>, and the sum of the elements in <code>mid</code> is less than or equal to the sum of the elements in <code>right</code>.</li>
</ul>

<p>Given <code>nums</code>, an array of <strong>non-negative</strong> integers, return <em>the number of <strong>good</strong> ways to split</em> <code>nums</code>. As the number may be too large, return it <strong>modulo</strong> <code>10<sup>9 </sup>+ 7</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [1,1,1]
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only good way to split nums is [1] [1] [1].</pre>

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

<pre>
<strong>Input:</strong> nums = [1,2,2,2,5,0]
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are three good ways of splitting nums:
[1] [2] [2,2,5,0]
[1] [2,2] [2,5,0]
[1,2] [2,2] [5,0]
</pre>

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

<pre>
<strong>Input:</strong> nums = [3,2,1]
<strong>Output:</strong> 0
<strong>Explanation:</strong> There is no good way to split nums.</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>3 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def waysToSplit(self, nums: List[int]) -> int:
        
        prefix = [0] * len(nums)

        cur = 0

        for i in range(len(nums)):
            cur += nums[i]
            prefix[i] = cur
        
        # 1 2 3 4 5 6 7 8
        #   i       m    
        res = 0
        for i in range(len(nums)-2):

            # BS to find the possible starting point of the third partition
            
            start = -1
            end = -1

            l = i + 2
            r = len(nums)

            while l < r:

                mid = (l+r) // 2

                if (prefix[mid-1]-prefix[i] >= prefix[i]):
                    r = mid
                else:
                    l = mid + 1
                
            start = l
            
            l = i + 2
            r = len(nums)

            while l < r:
                mid = (l+r) // 2
                
                if not (prefix[-1]-prefix[mid-1] >= prefix[mid-1]-prefix[i]):
                    r = mid
                else:
                    l = mid + 1
            
            end = l-1

            if end-start+1 > 0:
                
                res += end-start+1
        
        return res % (10**9+7)

            
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