<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:
        n = len(nums)
        prefixSum = [0 for _ in range(n)]
        prefixSum[0] = nums[0]
        for i in range(1,n):
            prefixSum[i] = prefixSum[i-1] + nums[i]
        count = 0
        MOD = 10**9 + 7
        def binarySearch(index,searchLeft):
            start = index
            end = n-2
            result = -1
            leftSum = prefixSum[index-1]
            while start <= end:
                mid = start + (end-start) // 2
                midSum = prefixSum[mid]-prefixSum[index-1]
                rightSum = prefixSum[n-1] - prefixSum[mid]
                if leftSum <= midSum <= rightSum:
                    result = mid
                    if searchLeft:
                        end = mid - 1
                    else:
                        start = mid + 1
                elif leftSum > midSum:
                    start = mid + 1
                else:
                    end = mid - 1            
            return result                
        for i in range(1,n-1):
            if prefixSum[i-1] > (prefixSum[n-1] - prefixSum[i-1])//2:
                break
            leftPointer = binarySearch(i,True)
            rightPointer = binarySearch(i,False)
            if leftPointer == -1 or rightPointer == -1:
                continue
            count = (count + (rightPointer-leftPointer+1)%MOD)%MOD  
        return count    

        
1584