<p>Given an integer array <code>nums</code> and two integers <code>lower</code> and <code>upper</code>, return <em>the number of range sums that lie in</em> <code>[lower, upper]</code> <em>inclusive</em>.</p>

<p>Range sum <code>S(i, j)</code> is defined as the sum of the elements in <code>nums</code> between indices <code>i</code> and <code>j</code> inclusive, where <code>i &lt;= j</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [-2,5,-1], lower = -2, upper = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three ranges are: [0,0], [2,2], and [0,2] and their respective sums are: -2, -1, 2.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [0], lower = 0, upper = 0
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-2<sup>31</sup> &lt;= nums[i] &lt;= 2<sup>31</sup> - 1</code></li>
	<li><code>-10<sup>5</sup> &lt;= lower &lt;= upper &lt;= 10<sup>5</sup></code></li>
	<li>The answer is <strong>guaranteed</strong> to fit in a <strong>32-bit</strong> integer.</li>
</ul>

#pragma GCC optimize("O3", "unroll-loops")
static auto _ = [](){
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return nullptr;
}();
class Solution {
public:
    int fn(vector<long>& sum, int l, int u, int s, int e) {
        if(e-s <= 1) 
            return 0;
        int mid = (s+e)/2;
        int m=mid, n=mid, cnt=0;
        cnt = fn(sum, l, u, s, mid) + fn(sum, l, u, mid, e);
        for(int i=s; i<mid; i++) {
            while(m<e and sum[m]-sum[i] < l) 
                m++;
            while(n<e and sum[n]-sum[i] <= u) 
                n++;
            cnt += n-m;
        }
        inplace_merge(sum.begin()+s, sum.begin()+mid, sum.begin()+e);
        return cnt;
    }

    int countRangeSum(vector<int>& nums, int l, int u) {
        int len = nums.size();
        vector<long> sum(len + 1, 0);
        for(int i =0; i< len; i++) 
            sum[i+1] = sum[i]+nums[i];
        return fn(sum, l, u, 0, len+1);
    }
};
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