<p>You are given a list of strings of the <strong>same length</strong> <code>words</code> and a string <code>target</code>.</p>

<p>Your task is to form <code>target</code> using the given <code>words</code> under the following rules:</p>

<ul>
	<li><code>target</code> should be formed from left to right.</li>
	<li>To form the <code>i<sup>th</sup></code> character (<strong>0-indexed</strong>) of <code>target</code>, you can choose the <code>k<sup>th</sup></code> character of the <code>j<sup>th</sup></code> string in <code>words</code> if <code>target[i] = words[j][k]</code>.</li>
	<li>Once you use the <code>k<sup>th</sup></code> character of the <code>j<sup>th</sup></code> string of <code>words</code>, you <strong>can no longer</strong> use the <code>x<sup>th</sup></code> character of any string in <code>words</code> where <code>x &lt;= k</code>. In other words, all characters to the left of or at index <code>k</code> become unusuable for every string.</li>
	<li>Repeat the process until you form the string <code>target</code>.</li>
</ul>

<p><strong>Notice</strong> that you can use <strong>multiple characters</strong> from the <strong>same string</strong> in <code>words</code> provided the conditions above are met.</p>

<p>Return <em>the number of ways to form <code>target</code> from <code>words</code></em>. Since the answer may be too large, return it <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> words = [&quot;acca&quot;,&quot;bbbb&quot;,&quot;caca&quot;], target = &quot;aba&quot;
<strong>Output:</strong> 6
<strong>Explanation:</strong> There are 6 ways to form target.
&quot;aba&quot; -&gt; index 0 (&quot;<u>a</u>cca&quot;), index 1 (&quot;b<u>b</u>bb&quot;), index 3 (&quot;cac<u>a</u>&quot;)
&quot;aba&quot; -&gt; index 0 (&quot;<u>a</u>cca&quot;), index 2 (&quot;bb<u>b</u>b&quot;), index 3 (&quot;cac<u>a</u>&quot;)
&quot;aba&quot; -&gt; index 0 (&quot;<u>a</u>cca&quot;), index 1 (&quot;b<u>b</u>bb&quot;), index 3 (&quot;acc<u>a</u>&quot;)
&quot;aba&quot; -&gt; index 0 (&quot;<u>a</u>cca&quot;), index 2 (&quot;bb<u>b</u>b&quot;), index 3 (&quot;acc<u>a</u>&quot;)
&quot;aba&quot; -&gt; index 1 (&quot;c<u>a</u>ca&quot;), index 2 (&quot;bb<u>b</u>b&quot;), index 3 (&quot;acc<u>a</u>&quot;)
&quot;aba&quot; -&gt; index 1 (&quot;c<u>a</u>ca&quot;), index 2 (&quot;bb<u>b</u>b&quot;), index 3 (&quot;cac<u>a</u>&quot;)
</pre>

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

<pre>
<strong>Input:</strong> words = [&quot;abba&quot;,&quot;baab&quot;], target = &quot;bab&quot;
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 4 ways to form target.
&quot;bab&quot; -&gt; index 0 (&quot;<u>b</u>aab&quot;), index 1 (&quot;b<u>a</u>ab&quot;), index 2 (&quot;ab<u>b</u>a&quot;)
&quot;bab&quot; -&gt; index 0 (&quot;<u>b</u>aab&quot;), index 1 (&quot;b<u>a</u>ab&quot;), index 3 (&quot;baa<u>b</u>&quot;)
&quot;bab&quot; -&gt; index 0 (&quot;<u>b</u>aab&quot;), index 2 (&quot;ba<u>a</u>b&quot;), index 3 (&quot;baa<u>b</u>&quot;)
&quot;bab&quot; -&gt; index 1 (&quot;a<u>b</u>ba&quot;), index 2 (&quot;ba<u>a</u>b&quot;), index 3 (&quot;baa<u>b</u>&quot;)
</pre>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 1000</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 1000</code></li>
	<li>All strings in <code>words</code> have the same length.</li>
	<li><code>1 &lt;= target.length &lt;= 1000</code></li>
	<li><code>words[i]</code> and <code>target</code> contain only lowercase English letters.</li>
</ul>

class Solution {
public:
    long long helper(vector<vector<int>>&dp, string & target, int k,map<pair<int,int>,int>&h,int i,int m){ 
        if(k==target.size()){
            return 1;
        }
        if(i==m){
            return 0;
        }
        if(h.count({k,i})){
            return h[{k,i}];
        }
        long long ans=0;
        int a=target[k]-'a';
        ans+=helper(dp,target,k,h,i+1,m);
        if(dp[i][a]>0){
            ans+=dp[i][a]*helper(dp,target,k+1,h,i+1,m);
            ans%=1000000007;
        }  
        return h[{k,i}]=ans;
    }
    int numWays(vector<string>& words, string target) {
        int n=words.size();
        int m=0;
        for(string s:words){
            if(m<s.size()){
                m=s.size();
            }
        }
        vector<vector<int>>dp(m,vector<int>(26,0));
        for(string s:words){
            for(int i=0;i<s.size();i++){
                int a=s[i]-'a';
                dp[i][a]++;
            }
        }
        map<pair<int,int>,int>h;
        return helper(dp,target,0,h,0,m)%1000000007;
    }
};
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