<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=[0]*(len(nums)+1)
        for i in range(len(nums)):
            prefix[i+1]=nums[i]+prefix[i]

        def left(l,target):
            ind=l
            l=l
            r=len(nums)-2
            ans=None
            while l<=r:
                mid=(l+r)//2
                if (prefix[mid+1]-prefix[ind])>=target:
                    ans=mid
                    r=mid-1
                else:
                    l=mid+1
            return ans if ans!=None else l

        def right(l,target):
            ind=l
            l=l
            r=len(nums)-2
            rans=None
            while l<=r:
                mid=(l+r)//2
                if (prefix[mid+1]-prefix[ind])<=target:
                    rans=mid
                    l=mid+1
                else:
                    r=mid-1
            return rans if rans!=None else r

        total=0
        summ=0
        for i in range(len(nums)-2):
            summ+=nums[i]
            if summ>prefix[-1]//3:
                break
            mini=left(i+1,summ)
            rem=prefix[-1]-summ
            maxi=right(i+1,rem//2)
            #print(i,mini,maxi)
            check=maxi-mini+1
            if check>0:
                total+=check
            else:
                total+=0
            total=total % ((10 ** 9) + 7)
        return total%((10**9)+7)
1300