<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 {
private:
    int divide(vector<long> & prenum,int left, int right, int lower, int upper)
    {
        if(right - left <= 1)
        {
            if(right - left == 1)
            {
                int count = (lower <= prenum[right]-prenum[left] && prenum[right]-prenum[left] <= upper);
                if (prenum[left] > prenum[right])
                    swap(prenum[left],prenum[right]);
//                cout<<"left ="<<left<<" right= "<<right<<endl;
 //               printvector(prenum);
                return count;
            }
            else
            {
                return 0;
            }
        }
        int mid = (left + right) / 2;
        int count = 0;
        count += divide (prenum,left,mid,lower,upper);
        count += divide (prenum,mid+1,right,lower,upper);
        vector<long> temp(right-left+1);
        int r = mid +1;
        int t = 0;
        int j = mid+1;
        int k = mid+1;
        for (int i=left;i<=mid;i++)
        {
            while (j<=right && prenum[j]  < lower + prenum[i])
                j++;
            while (k<=right && prenum[k] <= upper + prenum[i] )
                k++;
            count += k-j;
            while (r<=right && prenum[i] > prenum[r]) temp[t++] = prenum[r++];
            temp[t++] = prenum[i];
        }
        while(r<=right) temp[t++] = prenum[r++];
//       cout<<"temp = :"<<endl;
//        printvector(temp);
       for (int t = 0;t<right-left+1;t++)
           prenum[left+t] = temp[t];
//        cout<<"left ="<<left<<" right= "<<right<<endl;
//       printvector(prenum);
        return count;
    }

public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        vector<long> presum(nums.size()+1,0);
        int n = nums.size();
        for (int i=1;i<=n;i++)
            presum[i] = presum[i-1] + nums[i-1];
//        printvector(presum);
        return divide(presum,0,n,lower,upper);
    }
};
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