<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 sum, 
        #since non negative integers, prefix sum will be sorted
        def binarySearch(target, left, right):
            ans = -1
            while left <= right:
                middle = (left+right) // 2
                
                if prefix[middle]>= target:
                    ans = middle
                    right = middle - 1
                else:
                    left = middle + 1
            return ans                



        count = 0
        prefix = [0]*len(nums)
        for i in range(len(nums)):
            if i == 0:
                prefix[i] = nums[i]
            else:
                prefix[i] = nums[i] + prefix[i-1]
        totalSum = prefix[-1]

        for i in range(len(nums) - 2):
            currSum = prefix[i]
            #calculate remaining Sum removing until curr 
            remaining = totalSum - currSum
            startVal = currSum
            if remaining % 2 == 0:
                endVal = remaining // 2 + 1
            else:
                endVal = ceil(remaining / 2)
            
            secondStartIndex = binarySearch(currSum*2, i+1, len(nums)-2)
            if secondStartIndex == -1:
                continue
            thirdSum = totalSum - prefix[secondStartIndex]
            secondSum = prefix[secondStartIndex] - prefix[i]
            if remaining != 0 and secondSum > remaining // 2:
                continue
            else:
                maxSecondIndex = binarySearch(currSum+endVal, i+1, len(nums)-1)
         
                thirdSum = totalSum - prefix[maxSecondIndex]
                if maxSecondIndex == secondStartIndex:
                    count += 1
                elif maxSecondIndex == -1:
                    maxSecondIndex = len(nums) - 1
                count += maxSecondIndex - secondStartIndex 
            
        return count %(10**9 + 7)
1507