<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 {
public:

    int mod = 1e9 + 7;
    string ss, se, ev;
    vector<int> lps;
    int dp[501][51];

    int solve(int pos, int evil_len, int lo, int hi) {
        if(evil_len == ev.size()) return 0; // prunning is done here since no need is there to explore rest of the string, since it wont contribute to result
        if(pos == ss.size()) return 1;

        int& val = dp[pos][evil_len];
        if((!lo && !hi) && val != -1) return val;

        int count = 0;
        char low = lo ? ss[pos] : 'a';
        char high = hi ? se[pos] : 'z';

        for(char i=low; i<=high; ++i) {
            int j = evil_len;
            while(j > 0 && ev[j] != i)
                j = lps[j-1];
            if(ev[j] == i) j++;
            count = (count + solve(pos + 1, j, lo & (i == ss[pos]), hi & (i == se[pos]))) % mod;
        } 

        return lo || hi ? count : val = count; 
    }

    int findGoodStrings(int n, string s1, string s2, string evil) {
        lps.assign(evil.size(), 0);
        ss = s1, se = s2, ev = evil;

        int j;
        for(int i=1; i<evil.size(); ++i) {
            j = lps[i-1];
            while(j > 0 && evil[i] != evil[j])
                j = lps[j-1];

            if(evil[i] == evil[j]) j++;
            lps[i] = j;
        }

        memset(dp, -1, sizeof(dp));
        
        return solve(0, 0, 1, 1);
    }
};
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