<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>

#define ll long long
class Solution {
public:
    ll mod_add(ll a, ll b, ll m) {a = a % m; b = b % m; return (((a + b) % m) + m) % m;}
    ll mod_sub(ll a, ll b, ll m){a = a % m;b = b % m;return (((a - b) % m) + m) % m;}
    ll mod_mul(ll a, ll b, ll m){a = a % m;b = b % m;return (((a * b) % m) + m) % m;}
    int totalStrength(vector<int>& strength) {
        const int MOD = 1e9 + 7;
        int n = strength.size();
        vector<ll> ps(n), pss(n);
        ps[0] = strength[0];
        for (int i = 1; i < n; ++i) ps[i] = ps[i - 1] + strength[i];
        pss[0] = ps[0];
        for (int i = 1; i < n; ++i) pss[i] = mod_add(pss[i - 1], ps[i], MOD);
        stack<int> st;
        ll stackSum = 0;
        vector<ll> dp(n + 1);
        ll ans = 0;
        dp[n] = 0;
        for (int i = n - 1; i >= 0; --i) {
            while (!st.empty() && strength[i] <= strength[st.top()]) {
                int k = st.top();
                st.pop();
                int w = (st.empty() ? n : st.top());
                ll v = (ll)strength[k] * (ll)(w - k);
                stackSum = mod_sub(stackSum, v, MOD);
            }
            int ind = (st.empty() ? n : st.top());
            int r = ind - 1, l = i;
            ll sumTillIIsMin = mod_sub(pss[r], (l > 0 ? pss[l - 1] : 0LL), MOD) - mod_mul((l > 0 ? ps[l - 1] : 0LL), (r - l + 1), MOD);
            ll mulSumTillIIsMin = mod_mul(sumTillIIsMin, strength[i], MOD);
            ll sumToAdd = ps[r] - (l > 0 ? ps[l - 1] : 0LL);
            ll reqSum = mod_mul(stackSum, sumToAdd, MOD);
            // ll extraSum = mod_mul(sumToAdd, (st.empty() ? 0LL : strength[st.top()]), MOD);
            // if (st.size() < n - ind) reqSum = mod_add(reqSum, mod_mul(extraSum, (n - ind - st.size()), MOD), MOD);
            ll totalSum = mod_add(mulSumTillIIsMin, reqSum, MOD);
            // cout << "i : " << i << " totalSum : " << totalSum << " mulSumTillIIsMin : " << mulSumTillIIsMin << " reqSum : " << reqSum << " stackSum : " << stackSum << " ind : " << ind << "\n";
            dp[i] = mod_add(totalSum, dp[ind], MOD);
            ans = mod_add(ans, dp[i], MOD);
            int g = (st.empty() ? n : st.top());
            st.push(i);
            ll u = (ll)strength[i] * (ll)(g - i);
            stackSum = mod_add(stackSum, u, MOD);
        }
        // cout << "dp : ";
        // for (auto it : dp) cout << it << " ";
        // cout << "\n";
        return ans;
    }
};
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