<p>You are given an array of strings <code>words</code> and a string <code>target</code>.</p>

<p>A string <code>x</code> is called <strong>valid</strong> if <code>x</code> is a <span data-keyword="string-prefix">prefix</span> of <strong>any</strong> string in <code>words</code>.</p>

<p>Return the <strong>minimum</strong> number of <strong>valid</strong> strings that can be <em>concatenated</em> to form <code>target</code>. If it is <strong>not</strong> possible to form <code>target</code>, return <code>-1</code>.</p>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abc&quot;,&quot;aaaaa&quot;,&quot;bcdef&quot;], target = &quot;aabcdabc&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">3</span></p>

<p><strong>Explanation:</strong></p>

<p>The target string can be formed by concatenating:</p>

<ul>
	<li>Prefix of length 2 of <code>words[1]</code>, i.e. <code>&quot;aa&quot;</code>.</li>
	<li>Prefix of length 3 of <code>words[2]</code>, i.e. <code>&quot;bcd&quot;</code>.</li>
	<li>Prefix of length 3 of <code>words[0]</code>, i.e. <code>&quot;abc&quot;</code>.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abababab&quot;,&quot;ab&quot;], target = &quot;ababaababa&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p>The target string can be formed by concatenating:</p>

<ul>
	<li>Prefix of length 5 of <code>words[0]</code>, i.e. <code>&quot;ababa&quot;</code>.</li>
	<li>Prefix of length 5 of <code>words[0]</code>, i.e. <code>&quot;ababa&quot;</code>.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">words = [&quot;abcdef&quot;], target = &quot;xyz&quot;</span></p>

<p><strong>Output:</strong> <span class="example-io">-1</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= words.length &lt;= 100</code></li>
	<li><code>1 &lt;= words[i].length &lt;= 5 * 10<sup>3</sup></code></li>
	<li>The input is generated such that <code>sum(words[i].length) &lt;= 10<sup>5</sup></code>.</li>
	<li><code>words[i]</code> consists only of lowercase English letters.</li>
	<li><code>1 &lt;= target.length &lt;= 5 * 10<sup>3</sup></code></li>
	<li><code>target</code> consists only of lowercase English letters.</li>
</ul>

class Solution:
    def minValidStrings(self, words: List[str], target: str) -> int:
        n=len(target)
        mod=2**63-1
        iv=pow(27,-1,mod)
        f=lambda x:ord(x)-ord("a")+1
        def radr(x,c):
            return (x*27+c)%mod
        def subl(x,c,p):
            return (x-c*p)%mod
        def subr(x,c):
            return ((x-c)*iv)%mod
        s=set()
        for w in words:
            x=0
            for c in w:
                x=radr(x,f(c))
                s.add(x)
        
        
        cur=0
        left=[-1]*n
        beg=0
        p=1
        for i in range(n):
            cur=radr(cur,f(target[i]))
            
            while cur not in s:
                cur=subl(cur,f(target[beg]),p)
                beg+=1
                p=(p*iv)%mod
                if beg>i:break
            else:
                left[i]=beg
            p=(p*27)%mod
        
        mem=[-2]*n
        def g(r):
            if mem[r]!=-2:
                return mem[r]
            if T[r] in s:
                return 1
            else:
                l=left[r]
                if l==-1:
                    res=inf
                else:
                    res=1+min(g(v)for v in range(l-1,r))
                mem[r]=res
                return res
        t=0
        T=[0]*n
        for i,e in enumerate(target):
            t=radr(t,f(e))
            T[i]=t
        #print(n)
        #print(left)
        res=g(n-1)
        #return 0
        return res if res!=inf else -1
        
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