<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>

from bisect import bisect_left


# i: first index: left = nums[:i]
# j: second index: mid = nums[i:j]
# k: third index: right= nums[j:]
class Solution:
    def waysToSplit(self, nums: List[int]) -> int:
        prefix = [nums[0]]
        for x in nums[1:]:
            prefix.append(prefix[-1] + x)
        print(nums, prefix)
        ans = 0
        n = len(nums)
        print(f"{n = }")

        for i in range(n - 2):
            sum_i = prefix[i]
            j = bisect_left(prefix, 2 * sum_i, lo=i + 1)
            middle = (prefix[i] + prefix[-1]) // 2
            k = bisect_right(prefix, middle, hi=n-1)

            # print(f"{prefix[i] = }, {prefix[-1] = }")
            # print(f"{i = }, {sum_i = }, {2 * sum_i = }, {j = }, {k = }")
            # print(f"j: {nums[:j]} k: {nums[:k]}")
            # print(f"{middle = }, {i = }, {j = }, {k = }, {nums[k-1:] = }")
            if j > n - 1:
                continue

            if j >= k:
                continue

            ans += k - j
        return ans % int(1e9 + 7)


# sum_k - sum_i <= sum_n - sum_k
# 2*sum_k <= sum_n + sum_i
# sum_k <= (sum_n + sum_i)//2
# sum_i <= sum_j - sum_i
# 2*sum_i <= sum_j

# sum_k - sum_i <= sum_n - sum_k

990