<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:
        # Define the modulo as required by the problem statement
        MOD = 10**9 + 7
        
        # Calculate the prefix sums of the array
        prefix_sum = [0] * len(nums)
        prefix_sum[0] = nums[0]
        for i in range(1, len(nums)):
            prefix_sum[i] = prefix_sum[i - 1] + nums[i]
        
        # Initialize the result to 0
        result = 0
        
        # Iterate through the first split point (left end) from index 0 to len(nums) - 3
        for i in range(len(nums) - 2):
            # We need to find the first valid j such that:
            # prefix_sum[i] <= prefix_sum[j] - prefix_sum[i]
            # Use binary search or two pointers to find the smallest valid j
            left = i + 1
            right = len(nums) - 2
            while left <= right:
                mid = (left + right) // 2
                if prefix_sum[mid] - prefix_sum[i] >= prefix_sum[i]:
                    right = mid - 1
                else:
                    left = mid + 1
            j = left

            # We need to find the first invalid k such that:
            # prefix_sum[k] - prefix_sum[i] > prefix_sum[-1] - prefix_sum[k]
            # Use binary search or two pointers to find the largest valid k
            left = j
            right = len(nums) - 2
            while left <= right:
                mid = (left + right) // 2
                if prefix_sum[-1] - prefix_sum[mid] >= prefix_sum[mid] - prefix_sum[i]:
                    left = mid + 1
                else:
                    right = mid - 1
            k = right

            # If j is valid, count the number of valid (j, k) pairs
            if j <= k:
                result = (result + (k - j + 1)) % MOD
        
        # Return the result, ensuring it's modulo 10^9 + 7
        return result
1610