<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:
    struct segtree {
        vector<long long> st;
        long long n;

        segtree(long long size) {
            n = size;
            st.resize(4 * n, 0);
        }

        void update(long long indx, long long start, long long end, long long node) {
            if (start == end) {
                st[node] += 1;
                return;
            }

            long long mid = (start + end) / 2;
            if (indx <= mid) {
                update(indx, start, mid, 2 * node + 1);
            } else {
                update(indx, mid + 1, end, 2 * node + 2);
            }

            st[node] = st[2 * node + 1] + st[2 * node + 2];
        }

        int query(int l, int r, int start, int end, long long node) {
            if (start > r || end < l) {
                return 0;
            }

            if (l<=start && r>=end) {
                return st[node];
            }

            int mid = (start + end) / 2;
            int q1 = query(l, r, start, mid, 2 * node + 1);
            int q2 = query(l, r, mid + 1, end, 2 * node + 2);

            return q1 + q2;
        }
    };

    int countRangeSum(vector<int>& nums, int lower, int upper) {
        int n = nums.size();
        vector<long long> prefix(n+1,0);
        for(int i=0;i<n;i++){
            prefix[i+1]=prefix[i]+nums[i];
        }
        set<long long> s={0};
        for(long long sum:prefix){
            s.insert(sum);
            s.insert(sum-lower);
            s.insert(sum-upper);
        }
        unordered_map<long long, int > indexes;
        int ind=0;
        for(long long ele:s){
            indexes[ele]=ind;
            ind++;
        }
        long long ans=0;
        segtree tree(ind);
        for (long long sum : prefix) {
            long long l = sum-upper;
            long long h = sum-lower;
            ans += tree.query(indexes[l], indexes[h], 0, ind - 1, 0);
            tree.update(indexes[sum] , 0, ind - 1, 0);
        }

        return ans;
    }
};

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