<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>

using ll = long long;

class Solution {
public:

    static constexpr int nm = 100002;

    ll sum[nm];
    int n;

    int mergeSort(int l, int r, int lower, int upper) {
        if (l == r) return 0;
        int mid = (l + r) / 2;
        int res = mergeSort(l, mid, lower, upper) + mergeSort(mid + 1, r, lower, upper);
        for (int i = l, j = mid + 1, j2 = mid + 1; i <= mid; ++i) {
            while (j <= r && sum[j] - sum[i] < lower) j++;
            while (j2 <= r && sum[j2] - sum[i] <= upper) j2++;
            res += j2 - j;
        }

        vector<ll> tmp;
        for (int i = l, j = mid + 1; i <= mid || j <= r; ) {
            if (j > r || (i <= mid && sum[i] <= sum[j])) tmp.push_back(sum[i++]);
            else tmp.push_back(sum[j++]);
        }
        for (int i = l; i <= r; ++i) sum[i] = tmp[i - l];
        return res;
    }

    int countRangeSum(vector<int>& nums, int lower, int upper) {
        int n = nums.size();
        for (int i = 1; i <= n; ++i) sum[i] = sum[i - 1] + nums[i - 1];

        return mergeSort(0, n, lower, upper);
    }
};
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