<p>You are <strong>building</strong> a string <code>s</code> of length <code>n</code> <strong>one</strong> character at a time, <strong>prepending</strong> each new character to the <strong>front</strong> of the string. The strings are labeled from <code>1</code> to <code>n</code>, where the string with length <code>i</code> is labeled <code>s<sub>i</sub></code>.</p>

<ul>
	<li>For example, for <code>s = &quot;abaca&quot;</code>, <code>s<sub>1</sub> == &quot;a&quot;</code>, <code>s<sub>2</sub> == &quot;ca&quot;</code>, <code>s<sub>3</sub> == &quot;aca&quot;</code>, etc.</li>
</ul>

<p>The <strong>score</strong> of <code>s<sub>i</sub></code> is the length of the <strong>longest common prefix</strong> between <code>s<sub>i</sub></code> and <code>s<sub>n</sub></code> (Note that <code>s == s<sub>n</sub></code>).</p>

<p>Given the final string <code>s</code>, return<em> the <strong>sum</strong> of the <strong>score</strong> of every </em><code>s<sub>i</sub></code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;babab&quot;
<strong>Output:</strong> 9
<strong>Explanation:</strong>
For s<sub>1</sub> == &quot;b&quot;, the longest common prefix is &quot;b&quot; which has a score of 1.
For s<sub>2</sub> == &quot;ab&quot;, there is no common prefix so the score is 0.
For s<sub>3</sub> == &quot;bab&quot;, the longest common prefix is &quot;bab&quot; which has a score of 3.
For s<sub>4</sub> == &quot;abab&quot;, there is no common prefix so the score is 0.
For s<sub>5</sub> == &quot;babab&quot;, the longest common prefix is &quot;babab&quot; which has a score of 5.
The sum of the scores is 1 + 0 + 3 + 0 + 5 = 9, so we return 9.</pre>

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

<pre>
<strong>Input:</strong> s = &quot;azbazbzaz&quot;
<strong>Output:</strong> 14
<strong>Explanation:</strong> 
For s<sub>2</sub> == &quot;az&quot;, the longest common prefix is &quot;az&quot; which has a score of 2.
For s<sub>6</sub> == &quot;azbzaz&quot;, the longest common prefix is &quot;azb&quot; which has a score of 3.
For s<sub>9</sub> == &quot;azbazbzaz&quot;, the longest common prefix is &quot;azbazbzaz&quot; which has a score of 9.
For all other s<sub>i</sub>, the score is 0.
The sum of the scores is 2 + 3 + 9 = 14, so we return 14.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

#include <bits/stdc++.h>
using namespace std;
using ll = long long;

const ll BASE = 31;
const ll MOD = 1e9+7;


class Solution {
public:
    vector<ll> computePowers(int n) {
        vector<ll> powers(n);
        powers[0] = 1;
        for(int i = 1; i < n; i++) {
            powers[i] = (powers[i - 1] * BASE) % MOD;
        }
        return powers;
    }

    vector<ll> computeHash(const string& s) {
        vector<ll> h(s.size());
        h[0] = s[0] - 'a' + 1; // Convert 'a' to 1, 'b' to 2, etc.
        for(int i = 1; i < s.size(); i++) {
            h[i] = (h[i-1] * BASE + (s[i] - 'a' + 1)) % MOD;
        }
        return h;
    }

    ll getHash(int i, int j, const vector<ll>& h, const vector<ll>& powers) {
        if (i == 0) return h[j];
        return (h[j] - (h[i - 1] * powers[j - i + 1] % MOD) + MOD) % MOD;
    }

    ll computeHashString(const string& a) {
        vector<ll> p = computePowers(a.size());
        vector<ll> h = computeHash(a);
        return getHash(0, a.size() - 1, h, p);
    }


    long long sumScores(string s) {
        int n = s.length();
        vector<ll> powers = computePowers(n);
        vector<ll> hash = computeHash(s);
        
        long long totalScore = 0;
        
        for (int i = 0; i < n; i++) {
            int left = 0, right = n - i;
            while (left < right) {
                int mid = left + (right - left + 1) / 2;
                if (getHash(0, mid - 1, hash, powers) == getHash(i, i + mid - 1, hash, powers)) {
                    left = mid;
                } else {
                    right = mid - 1;
                }
            }
            totalScore += left;
        }
        
        return totalScore;
    }
};
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