<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:
        MOD = 10**9 + 7
        n = len(nums)
        prefix_sum = [0] * n
        prefix_sum[0] = nums[0]
        for i in range(1, n):
            prefix_sum[i] = prefix_sum[i - 1] + nums[i]

        def prefix(i):
            return prefix_sum[i]

        def suffix(i):
            return prefix_sum[-1] - prefix_sum[i - 1]

        total = 0
        for i in range(1, n - 1):
            if prefix(i - 1) > suffix(i):
                break
            left, right = i, n - 2
            while left < right:
                mid = (left + right) // 2
                if prefix(mid) >= 2 * prefix(i - 1):
                    right = mid
                else:
                    left = mid + 1
            j = right
            if prefix(j) < 2 * prefix(i - 1):
                continue
            left, right = i, n - 2
            while left < right:
                mid = (left + right) // 2
                if suffix(mid + 1) >= prefix(mid) - prefix(i - 1):
                    left = mid + 1
                else:
                    right = mid
            k = left
            if suffix(k + 1) < prefix(k) - prefix(i - 1):
                k -= 1
            total = (total + max(0, k - j + 1)) % MOD

        return total
2205