<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();
        long long prefixSum[n];
        int mod = 1e9 + 7;
        memset(prefixSum, 0, sizeof(prefixSum));
        prefixSum[0] = nums[0];
        for(int i = 1; i < n; i++){
            prefixSum[i] = prefixSum[i - 1] + nums[i];
        }

        int ways = 0;
        for(int mid = 1; mid < n - 1; mid++){
            int low = mid + 1; 
            int high = n - 1;
            int start = -1, end = -1;
            long long leftSum = prefixSum[mid - 1];
            while(low <= high){
                int right = low + (high - low)/2;
                long long rightSum = prefixSum[n - 1] - prefixSum[right - 1];
                long long midSum = prefixSum[n - 1] - (leftSum + rightSum);
                if(leftSum <= midSum && midSum <= rightSum){
                    start = right;
                    high = right - 1;
                }
                if(leftSum > midSum){
                    low = right + 1;
                }
                else if(midSum > rightSum){
                    high = right - 1;
                }
            }

            low = mid + 1;
            high = n - 1;
            while(low <= high){
                int right = low + (high - low)/2;
                long long rightSum = prefixSum[n - 1] - prefixSum[right - 1];
                long long midSum = prefixSum[n - 1] - (leftSum + rightSum);
                if(leftSum <= midSum && midSum <= rightSum){
                    end = right;
                    low = right + 1;
                }
                if(leftSum > midSum){
                    low = right + 1;
                }
                else if(midSum > rightSum){
                    high = right - 1;
                }
            }
            if(end != -1 && start != -1){
                ways = (ways + end - start + 1)%mod;
            }                        
        }

        return ways;
    }
};
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