<p>You are given a <strong>0-indexed</strong> array of <strong>unique</strong> strings <code>words</code>.</p>

<p>A <strong>palindrome pair</strong> is a pair of integers <code>(i, j)</code> such that:</p>

<ul>
	<li><code>0 &lt;= i, j &lt; words.length</code>,</li>
	<li><code>i != j</code>, and</li>
	<li><code>words[i] + words[j]</code> (the concatenation of the two strings) is a <span data-keyword="palindrome-string">palindrome</span>.</li>
</ul>

<p>Return <em>an array of all the <strong>palindrome pairs</strong> of </em><code>words</code>.</p>

<p>You must write an algorithm with&nbsp;<code>O(sum of words[i].length)</code>&nbsp;runtime complexity.</p>

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

<pre>
<strong>Input:</strong> words = [&quot;abcd&quot;,&quot;dcba&quot;,&quot;lls&quot;,&quot;s&quot;,&quot;sssll&quot;]
<strong>Output:</strong> [[0,1],[1,0],[3,2],[2,4]]
<strong>Explanation:</strong> The palindromes are [&quot;abcddcba&quot;,&quot;dcbaabcd&quot;,&quot;slls&quot;,&quot;llssssll&quot;]
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;bat&quot;,&quot;tab&quot;,&quot;cat&quot;]
<strong>Output:</strong> [[0,1],[1,0]]
<strong>Explanation:</strong> The palindromes are [&quot;battab&quot;,&quot;tabbat&quot;]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> words = [&quot;a&quot;,&quot;&quot;]
<strong>Output:</strong> [[0,1],[1,0]]
<strong>Explanation:</strong> The palindromes are [&quot;a&quot;,&quot;a&quot;]
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 5000</code></li>
	<li><code>0 &lt;= words[i].length &lt;= 300</code></li>
	<li><code>words[i]</code> consists of lowercase English letters.</li>
</ul>

typedef long long ll;
    
static const ll maxn = 305;
static const ll mod = (int)1e9 + 7;
static const ll p = 131;
static ll pi[maxn];
static ll hf[5005];
static ll hb[5005];

static int init () {
    pi[0] = 1;
    for (int i = 1; i < maxn; i++) pi[i] = pi[i - 1] * p % mod;
    return 0;
}

class Solution {
public:
    vector<vector<int>> palindromePairs(vector<string>& words) {
        static int _ = init();
        int n = words.size();
        fill(hf, hf + n, 0);
        fill(hb, hb + n, 0);
        for (int i = 0; i < n; i++) {
//            hf[i] = hb[i] = 0;
            string& s = words[i];
            ll len = s.size();
            for (int j = 0; j < len; j++) {
                hf[i] = (hf[i] * p + s[j]) % mod;
                hb[i] = (hb[i] * p + s[len - j - 1]) % mod;
            }
        }
        vector<vector<int>> ans;
        for (int i = 0; i < n; i++) {
            for (int j = i + 1; j < n; j++) {
                if (is_palindrome(words, i, j)) ans.push_back({i, j});
                if (is_palindrome(words, j, i)) ans.push_back({j, i});
            }
        }
        return ans;
    }

private:
    bool is_palindrome (vector<string>& words, int i, int j) {
        ll f = (hf[i] * pi[words[j].size()] + hf[j]) % mod;
        ll b = (hb[j] * pi[words[i].size()] + hb[i]) % mod;
        return f == b;
    }
};
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