<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>

class Solution {
public:
    int dnc(int low, int high, int lower, int upper, vector<int>& nums) {
        if(low == high) {
            return (nums[low] >= lower && nums[low] <= upper) ? 1 : 0;
        }
        int mid = (low + high) / 2;
        int m = high - mid;
        vector<long> temp;
        long sum = 0;
        for(int i = mid + 1; i <= high; i++) {
            sum += nums[i];
            temp.emplace_back(sum);
        }
        sort(temp.begin(), temp.end());
        sum = 0;
        int cnt = 0;
        for(int i = mid; i >= low; i--) {
            sum += nums[i];
            cnt += findIdx(upper - sum + 0.5, temp) - findIdx(lower - sum - 0.5, temp);
        }
        return cnt + dnc(low, mid, lower, upper, nums) + dnc(mid + 1, high, lower, upper, nums);
    }
    int findIdx(double val, vector<long>& temp) {
        int l = 0, r = temp.size() - 1, mid = 0, res = 0;
        while(l <= r) {
            mid = (l + r) / 2;
            if(temp[mid] <= val) {
                l = mid + 1;
                res = l;
            } else {
                r = mid - 1;
            }
        }
        return res;
    }
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        return dnc(0, nums.size() - 1, lower, upper, nums);
    }
};
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