<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 {
public:
    int waysToSplit(vector<int>& nums) {
        int n = nums.size();
        int mod = 1e9 + 7;

        for(int i=1;i<n;i++){
            nums[i]+=nums[i-1];}

        int count = 0;

        for(int i=0;i<=n-1;i++)
        {
            //we need to have at least one element in the 1st and 3rd group so we consider lo=i+1 && hi=n-2
            int lo=i+1,hi=n-2,right=-1,left=-1;
    
            //we calculate the right-most valid index
            while(lo<=hi)
            {
                int mid=lo+(hi-lo)/2;
                if(nums[mid]-nums[i]<=nums.back()-nums[mid])
                {
                    right=mid;
                    lo=mid+1;
                }
                else
                    hi=mid-1;
            }

        lo=i+1;hi=n-2;
            //we calculate the left-most valid index
             while(lo<=hi)
            {
                int mid=lo+(hi-lo)/2;
                if(nums[i]<=nums[mid]-nums[i])
                {
                    left=mid;
                    hi=mid-1;
                }
                else
                    lo=mid+1;
            }
            //invalid condition check i.e. if one of the bound does not exist 
            //or left bound is greater than right bound
            if(left==-1||right==-1||left>right)continue;
            
            count=(count+(right-left+1)%mod)%mod;
        }
        return count%mod;
        
    }
};
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