<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 seg_tree
{
public:
    vector<int> seg;

    seg_tree(int n) {
        seg.resize(4 * n + 1, 0);
    }

    void update(int ind, int low, int high, int idx) {
        if (low == high) {
            seg[ind] += 1;
            return;
        }

        int mid = (low + high) / 2;
        if (idx <= mid) {
            update(2 * ind + 1, low, mid, idx);
        } else {
            update(2 * ind + 2, mid + 1, high, idx);
        }

        seg[ind] = seg[2 * ind + 1] + seg[2 * ind + 2];
    }

    int query(int ind, int low, int high, int l, int r) {
        if (r < low || high < l) return 0;
        if (l <= low && high <= r) return seg[ind];

        int mid = (low + high) / 2;
        int left = query(2 * ind + 1, low, mid, l, r);
        int right = query(2 * ind + 2, mid + 1, high, l, r);
        return left + right;
    }
};

class Solution {
public:
    int countRangeSum(vector<int>& nums, int lower, int upper) {
        vector<long long> presums = {0};
        for (int num : nums) {
            presums.push_back(presums.back() + num);
        }

        set<long long> all_sums;
        for (long long presum : presums) {
            all_sums.insert(presum);
            all_sums.insert(presum - upper);
            all_sums.insert(presum - lower);
        }

        map<long long, int> sums_to_idx;
        int idx = 0;
        for (long long sum : all_sums) {
            sums_to_idx[sum] = idx++;
        }

        seg_tree st(idx);
        int result = 0;
        for (long long presum : presums) {
            int low = sums_to_idx[presum - upper];
            int high = sums_to_idx[presum - lower];
            result += st.query(0, 0, idx - 1, low, high);
            st.update(0, 0, idx - 1, sums_to_idx[presum]);
        }

        return result;
    }
};
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