<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 f(int left, int n, vector<int> &P, int t) {
        int l=left+1, h=n-2, m, ans=-1;
        while (l<=h) {
            m = (l+h)/2;
            if(P[m]-P[left]>=t){
                ans=m;
                h=m-1;
            } else {
                l=m+1;
            }
        }
        return ans;
    }
    int g(int left, int n, vector<int> &P, int t) {
        int l=left+1, h= n-2, m, ans=-1;
        while(l<=h){
            m=(l+h)/2;
            if(P[m]-P[left]<=t){
                ans=m;
                l=m+1;
            } else {
                h=m-1;
            }
        }
        return ans;
    }
    int waysToSplit(vector<int>& A) {
        int n=A.size();
        vector<int> p(n) ;
        p[0]=A[0];
        for(int i=1;i<n;i++) p[i]=p[i-1]+A[i];
        long res=0;
        const int mod=1e9+7;
        for(int i=0;i<n-2;i++){
            if(p[i]*3>p[n-1]) break;
            int rs=p[n-1]-p[i];
            int li=f(i, n, p, p[i]);
            int ri=g(i, n, p, rs/2);
            if(li==-1 or ri==-1) break;
            res+=(ri-li+1)%mod;
        }
        return res%mod;
    }
};
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