<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 findMidStart(int left, int n, vector<int> &prefixSum, int target) {
        int lo = left + 1, hi = n - 2, mid, ans = -1;
        while (lo <= hi) {
            mid = lo + (hi - lo) / 2;
            if (prefixSum[mid] - prefixSum[left] >= target) {
                ans = mid;
                hi = mid - 1;
            } else {
                lo = mid + 1;
            }
        }
        return ans;
    }
    int findMidEnd(int left, int n, vector<int> &prefixSum, int target) {
        int lo = left + 1, hi = n - 2, mid, ans = -1;
        while (lo <= hi) {
            mid = lo + (hi - lo) / 2;
            if (prefixSum[mid] - prefixSum[left] <= target) {
                ans = mid;
                lo = mid + 1;
            } else {
                hi = mid - 1;
            }
        }
        return ans;
    }
    int waysToSplit(vector<int>& nums) {
        int n = nums.size(), leftSum, remainingSum, midStart, midEnd, ans = 0, mod = 1e9 + 7;
        vector<int> prefixSum(n);
        prefixSum[0] = nums[0];
        for (int i = 1; i < n; i++) {
            prefixSum[i] = prefixSum[i - 1] + nums[i];
        }
        for (int left = 0; left < n - 2; left++) {
            leftSum = prefixSum[left];
            if (leftSum * 3 > prefixSum[n - 1]) {
                break;
            }
            remainingSum = prefixSum[n - 1] - prefixSum[left];
            midStart = findMidStart(left, n, prefixSum, leftSum);
            midEnd = findMidEnd(left, n, prefixSum, remainingSum / 2);
            if (midStart == -1 || midEnd == -1)
                break;
            ans = (ans + midEnd - midStart + 1) % mod;
        }
        return ans % mod;
    }
};
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