<p>Given the strings <code>s1</code> and <code>s2</code> of size <code>n</code> and the string <code>evil</code>, return <em>the number of <strong>good</strong> strings</em>.</p>

<p>A <strong>good</strong> string has size <code>n</code>, it is alphabetically greater than or equal to <code>s1</code>, it is alphabetically smaller than or equal to <code>s2</code>, and it does not contain the string <code>evil</code> as a substring. Since the answer can be a huge number, return this <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> n = 2, s1 = &quot;aa&quot;, s2 = &quot;da&quot;, evil = &quot;b&quot;
<strong>Output:</strong> 51 
<strong>Explanation:</strong> There are 25 good strings starting with &#39;a&#39;: &quot;aa&quot;,&quot;ac&quot;,&quot;ad&quot;,...,&quot;az&quot;. Then there are 25 good strings starting with &#39;c&#39;: &quot;ca&quot;,&quot;cc&quot;,&quot;cd&quot;,...,&quot;cz&quot; and finally there is one good string starting with &#39;d&#39;: &quot;da&quot;.&nbsp;
</pre>

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

<pre>
<strong>Input:</strong> n = 8, s1 = &quot;leetcode&quot;, s2 = &quot;leetgoes&quot;, evil = &quot;leet&quot;
<strong>Output:</strong> 0 
<strong>Explanation:</strong> All strings greater than or equal to s1 and smaller than or equal to s2 start with the prefix &quot;leet&quot;, therefore, there is not any good string.
</pre>

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

<pre>
<strong>Input:</strong> n = 2, s1 = &quot;gx&quot;, s2 = &quot;gz&quot;, evil = &quot;x&quot;
<strong>Output:</strong> 2
</pre>

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

<ul>
	<li><code>s1.length == n</code></li>
	<li><code>s2.length == n</code></li>
	<li><code>s1 &lt;= s2</code></li>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= evil.length &lt;= 50</code></li>
	<li>All strings consist of lowercase English letters.</li>
</ul>

class Solution {
    int mod = 1e9 + 7;
    vector<vector<vector<vector<int>>>> cache;

    vector<int> getkmp(const string &s) {
        int n = s.size();
        vector<int> kmp(n, 0);
        int i = 1, j = 0;

        while (i < n) {
            if (s[i] == s[j]) {
                kmp[i] = j + 1;
                i++;
                j++;
            } else {
                if (j > 0) j = kmp[j - 1];
                else i++;
            }
        }
        return kmp;
    }

    int solve(int i, int j, bool b1, bool b2, int n, 
              const string &s1, const string &s2, const string &evil, const vector<int> &kmp) {
        if (j >= evil.size()) return 0;
        if (i >= n) return 1;

        if (cache[i][j][b1][b2] != -1) return cache[i][j][b1][b2];

        char lb = b1 ? s1[i] : 'a';
        char ub = b2 ? s2[i] : 'z';

        int ans = 0;
        for (char c = lb; c <= ub; c++) {
            int k = j;
            while (k > 0 && evil[k] != c) k = kmp[k - 1];
            if (c == evil[k]) k++;
            ans = (ans + solve(i + 1, k, b1 && c == lb, b2 && c == ub, n, s1, s2, evil, kmp)) % mod;
        }

        cache[i][j][b1][b2] = ans;
        return ans;
    }

public:
    int findGoodStrings(int n, const string &s1, const string &s2, const string &evil) {
        vector<int> kmp = getkmp(evil);
        cache = vector<vector<vector<vector<int>>>>(
            n, vector<vector<vector<int>>>(
                evil.size(), vector<vector<int>>(2, vector<int>(2, -1))
            )
        );
        return solve(0, 0, 1, 1, n, s1, s2, evil, kmp);
    }
};

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