<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:
        n = len(nums)
        total = sum(nums)

        prefix = [0] * (n+1)
        for i in range(n):
            prefix[i+1] = prefix[i] + nums[i]
        
        def search1(idx):
            prev_sum = prefix[idx+1]

            l = idx + 1
            r = n - 1

            if prefix[-1] < 3*prev_sum:
                return -1

            while l < r:
                m = (l+r) // 2
                m_sum = prefix[m+1] 

                if m_sum < 2 * prev_sum:
                    l = m + 1
                else:
                    r = m
            
            return l
        
        def search2(idx):
            prev_sum = prefix[idx+1]
            l = idx + 1
            r = n - 2

            if l > r or prefix[l+1] - prev_sum > prefix[-1] - prefix[l+1]:
                return -1

            while l < r:
                m = (l+r+1) // 2
                m_sum = prefix[m + 1]

                if prefix[-1] - m_sum >= m_sum - prev_sum:
                    l = m
                else:
                    r = m - 1
            
            return l



        count = 0
        for i in range(n):
            f = search1(i)
            s = search2(i)

            # print(i, f, s)
            
            if f == -1 or s == -1:
                continue
            
            if f > s:
                continue
            
            count += s - f + 1
        return count % (10**9 + 7)

            
            

1714