<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>

#define ll long long
class Solution {
public:
    ll mod=1e9+7;
    string l,r,e;
    ll  dp[501][2][2][51];
    vector<int>kmp;
    ll rec(int lev,int lt,int rt,int m){
        if(m==e.size())return 0;
        if(lev==l.size())return 1;
        auto &ans=dp[lev][lt][rt][m];
        if(ans!=-1)return ans;
        ans=0;char lo=(lt?l[lev]:'a'),hi=(rt?r[lev]:'z');
        for(char ch=lo;ch<=hi;ch++){
            int nlt=(lt&&(ch==lo)),nrt=(rt&&(ch==hi));
            int nm=m;
            while(nm&&e[nm]!=ch)nm=kmp[nm-1];// like KMP
            if(e[nm]==ch)nm++;
            ans=(ans+rec(lev+1,nlt,nrt,nm)%mod)%mod;
        }
        return ans;
    }
    int findGoodStrings(int n, string s1, string s2, string evil) {
        l=s1,r=s2,e=evil;
        memset(dp,-1,sizeof(dp));
        kmp.resize(evil.size(), 0);
        int m = evil.size();
        for (int i = 1; i < m; ++i) {
            int match = kmp[i - 1];
            while (match > 0 && evil[i] != evil[match])match = kmp[match - 1];
            if (evil[i] == evil[match])match++;
            kmp[i] = match;
        }
        return rec(0,1,1,0)%mod;
    }
};
9000