<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, suffix = [nums[0]]*len(nums), [nums[-1]]*len(nums)
        for i in range(1, len(nums)):
            prefix[i] = prefix[i-1] + nums[i]
        for i in range(len(nums)-2, -1, -1):
            suffix[i] = suffix[i+1] + nums[i]
        res, modulo = 0, 1000000007
        for leftEnd in range(0, len(nums)-2):
            if (suffix[leftEnd + 1] < (2*prefix[leftEnd])):
                continue
            # find smallest index for which mid >= left
            l, r = leftEnd + 1, len(nums)-1
            while (l < r-1):
                m = (l+r)//2
                if (prefix[m] - prefix[leftEnd] >= prefix[leftEnd]):
                    r = m
                else:
                    l = m
            if (prefix[l] - prefix[leftEnd] >= prefix[leftEnd]):
                r = l
            if (prefix[r] - prefix[leftEnd] > prefix[-1] - prefix[r]):
                continue
            lowest = r
            l, r = lowest, len(nums)-1
            while (l < r-1):
                m = (l+r)//2
                if (prefix[m] - prefix[leftEnd] <= prefix[-1] - prefix[m]):
                    l = m
                else:
                    r = m
            highest = l
            res += (highest - lowest + 1)
            res %= modulo
        return res



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