<p>As the ruler of a kingdom, you have an army of wizards at your command.</p>

<p>You are given a <strong>0-indexed</strong> integer array <code>strength</code>, where <code>strength[i]</code> denotes the strength of the <code>i<sup>th</sup></code> wizard. For a <strong>contiguous</strong> group of wizards (i.e. the wizards&#39; strengths form a <strong>subarray</strong> of <code>strength</code>), the <strong>total strength</strong> is defined as the <strong>product</strong> of the following two values:</p>

<ul>
	<li>The strength of the <strong>weakest</strong> wizard in the group.</li>
	<li>The <strong>total</strong> of all the individual strengths of the wizards in the group.</li>
</ul>

<p>Return <em>the <strong>sum</strong> of the total strengths of <strong>all</strong> contiguous groups of wizards</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>subarray</strong> is a contiguous <strong>non-empty</strong> sequence of elements within an array.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> strength = [1,3,1,2]
<strong>Output:</strong> 44
<strong>Explanation:</strong> The following are all the contiguous groups of wizards:
- [1] from [<u><strong>1</strong></u>,3,1,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1
- [3] from [1,<u><strong>3</strong></u>,1,2] has a total strength of min([3]) * sum([3]) = 3 * 3 = 9
- [1] from [1,3,<u><strong>1</strong></u>,2] has a total strength of min([1]) * sum([1]) = 1 * 1 = 1
- [2] from [1,3,1,<u><strong>2</strong></u>] has a total strength of min([2]) * sum([2]) = 2 * 2 = 4
- [1,3] from [<u><strong>1,3</strong></u>,1,2] has a total strength of min([1,3]) * sum([1,3]) = 1 * 4 = 4
- [3,1] from [1,<u><strong>3,1</strong></u>,2] has a total strength of min([3,1]) * sum([3,1]) = 1 * 4 = 4
- [1,2] from [1,3,<u><strong>1,2</strong></u>] has a total strength of min([1,2]) * sum([1,2]) = 1 * 3 = 3
- [1,3,1] from [<u><strong>1,3,1</strong></u>,2] has a total strength of min([1,3,1]) * sum([1,3,1]) = 1 * 5 = 5
- [3,1,2] from [1,<u><strong>3,1,2</strong></u>] has a total strength of min([3,1,2]) * sum([3,1,2]) = 1 * 6 = 6
- [1,3,1,2] from [<u><strong>1,3,1,2</strong></u>] has a total strength of min([1,3,1,2]) * sum([1,3,1,2]) = 1 * 7 = 7
The sum of all the total strengths is 1 + 9 + 1 + 4 + 4 + 4 + 3 + 5 + 6 + 7 = 44.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> strength = [5,4,6]
<strong>Output:</strong> 213
<strong>Explanation:</strong> The following are all the contiguous groups of wizards: 
- [5] from [<u><strong>5</strong></u>,4,6] has a total strength of min([5]) * sum([5]) = 5 * 5 = 25
- [4] from [5,<u><strong>4</strong></u>,6] has a total strength of min([4]) * sum([4]) = 4 * 4 = 16
- [6] from [5,4,<u><strong>6</strong></u>] has a total strength of min([6]) * sum([6]) = 6 * 6 = 36
- [5,4] from [<u><strong>5,4</strong></u>,6] has a total strength of min([5,4]) * sum([5,4]) = 4 * 9 = 36
- [4,6] from [5,<u><strong>4,6</strong></u>] has a total strength of min([4,6]) * sum([4,6]) = 4 * 10 = 40
- [5,4,6] from [<u><strong>5,4,6</strong></u>] has a total strength of min([5,4,6]) * sum([5,4,6]) = 4 * 15 = 60
The sum of all the total strengths is 25 + 16 + 36 + 36 + 40 + 60 = 213.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= strength.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= strength[i] &lt;= 10<sup>9</sup></code></li>
</ul>

using ll = long long;
class Solution {
public:
    int n;
    int MOD = 1e9 + 7;
    vector<ll> prefix, prefix_sum;
    vector<ll> suffix, suffix_sum;

    ll get_total(int prev, int i, int next){
        int l = i - prev, r = next - i;
        // ll total = pow(prefix[n - 1], l * r);
        ll total = prefix[next - 1];
        if (prev != -1)
            total -= prefix[prev];
        total = (total + MOD) % MOD;
        total = total * l % MOD * r % MOD;
        // cout << i << " " << prev << " " <<  next << " " << total << '\n';
        ll num = 0;
        if (i - 1 >= 0)
            num = prefix_sum[i - 1];
        if (prev >= 0){
            num -= prefix_sum[prev];
            num -= prefix[prev] * (i - prev - 1);
        }
        num = (num % MOD + MOD) % MOD;
        total -= num * r;
        total = (total % MOD + MOD) % MOD;
        // cout << "   " << total << '\n';

        num = 0;
        if (i + 1 < n)
            num = suffix_sum[i + 1];
        if (next < n){
            num -= suffix_sum[next];
            num -= suffix[next] * (next - i - 1);
        }
        num = (num % MOD + MOD) % MOD;
        total -= num * l;
        total = (total % MOD + MOD) % MOD;

        // cout << "   " << total << '\n';

        return total % MOD;
    }
    int totalStrength(vector<int>& nums) {
        // int n = nums.size();
        this->n = nums.size();
        prefix.resize(n, 0), prefix_sum.resize(n, 0);
        prefix[0] = nums[0];
        prefix_sum[0] = prefix[0];
        for (int i = 1; i < n; i++){
            prefix[i] = (prefix[i - 1] + nums[i]) % MOD;
            prefix_sum[i] = (prefix_sum[i - 1] + prefix[i]) % MOD;
        }
        suffix.resize(n, 0), suffix_sum.resize(n, 0);
        suffix[n - 1] = nums[n - 1];
        suffix_sum[n - 1] = suffix[n - 1];
        for (int i = n - 2; i >= 0; i--){
            suffix[i] = (suffix[i + 1] + nums[i]) % MOD;
            suffix_sum[i] = (suffix_sum[i + 1] + suffix[i]) % MOD;
        }
        // cout << suffix_sum[1] << '\n';
        // for (int i = 0; i < n; i++)
        //     cout << prefix[i] << " " << prefix_sum[i] << " " << suffix[i] << " " << suffix_sum[i] << '\n';
        vector<int> prevSmaller(n, -1);
        vector<int> nextSmaller(n, n);        
        stack<int> s;
        for (int i = 0; i < n; i++){
            int num = nums[i];
            while (!s.empty() && num < nums[s.top()]){
                nextSmaller[s.top()] = i;
                s.pop();
            }
            s.push(i);
        }
        while (!s.empty())
            s.pop();
        for (int i = n - 1; i >= 0; i--){
            int num = nums[i];
            while (!s.empty() && num <= nums[s.top()]){
                prevSmaller[s.top()] = i;
                s.pop();
            }
            s.push(i);
        }
        ll res = 0;
        for (int i = 0; i < n; i++){
            ll ret = get_total(prevSmaller[i], i, nextSmaller[i]);
            // cout << i << " " << prevSmaller[i] << " " << nextSmaller[i] << " " << ret << '\n';
            ll num = nums[i] * ret % MOD;
            res = (res + num) % MOD;
        }
        return res;
    }
};
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