<p>You are given a string <code>target</code>, an array of strings <code>words</code>, and an integer array <code>costs</code>, both arrays of the same length.</p>

<p>Imagine an empty string <code>s</code>.</p>

<p>You can perform the following operation any number of times (including <strong>zero</strong>):</p>

<ul>
	<li>Choose an index <code>i</code> in the range <code>[0, words.length - 1]</code>.</li>
	<li>Append <code>words[i]</code> to <code>s</code>.</li>
	<li>The cost of operation is <code>costs[i]</code>.</li>
</ul>

<p>Return the <strong>minimum</strong> cost to make <code>s</code> equal to <code>target</code>. If it&#39;s not possible, 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">target = &quot;abcdef&quot;, words = [&quot;abdef&quot;,&quot;abc&quot;,&quot;d&quot;,&quot;def&quot;,&quot;ef&quot;], costs = [100,1,1,10,5]</span></p>

<p><strong>Output:</strong> <span class="example-io">7</span></p>

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

<p>The minimum cost can be achieved by performing the following operations:</p>

<ul>
	<li>Select index 1 and append <code>&quot;abc&quot;</code> to <code>s</code> at a cost of 1, resulting in <code>s = &quot;abc&quot;</code>.</li>
	<li>Select index 2 and append <code>&quot;d&quot;</code> to <code>s</code> at a cost of 1, resulting in <code>s = &quot;abcd&quot;</code>.</li>
	<li>Select index 4 and append <code>&quot;ef&quot;</code> to <code>s</code> at a cost of 5, resulting in <code>s = &quot;abcdef&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">target = &quot;aaaa&quot;, words = [&quot;z&quot;,&quot;zz&quot;,&quot;zzz&quot;], costs = [1,10,100]</span></p>

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

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

<p>It is impossible to make <code>s</code> equal to <code>target</code>, so we return -1.</p>
</div>

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

<ul>
	<li><code>1 &lt;= target.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words.length == costs.length &lt;= 5 * 10<sup>4</sup></code></li>
	<li><code>1 &lt;= words[i].length &lt;= target.length</code></li>
	<li>The total sum of <code>words[i].length</code> is less than or equal to <code>5 * 10<sup>4</sup></code>.</li>
	<li><code>target</code> and <code>words[i]</code> consist only of lowercase English letters.</li>
	<li><code>1 &lt;= costs[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution:
    def minimumCost(self, target: str, words: List[str], costs: List[int]) -> int:
        dic = {}
        for i in range(len(words)):
            if words[i] not in dic:
                dic[words[i]] = costs[i]
            dic[words[i]] = min(dic[words[i]], costs[i])
        words = []
        costs = []
        for word, cost in dic.items():
            words.append(word)
            costs.append(cost)

        n = len(target)
        M = 1000_000_007
        x = 257
        x_ = [1] * (n + 1)
        h = [0] * (n + 1)
        for i in range(n):
            x_[i + 1] = (x_[i] * x) % M
            h[i + 1] = (h[i] * x + ord(target[i])) % M
        
        words_dict = defaultdict(list)
        for i in range(len(words)):
            words_dict[words[i][0]].append([i, len(words[i])])
            h_word = 0
            for c in words[i]:
                h_word = (h_word * x + ord(c)) % M
            words[i] = h_word

        def get_hash(left, right):
            return (h[right] - h[left] * x_[right - left] + M) % M

        ans = [float("inf")] * (n + 1)
        ans[0] = 0
        for i in range(n):
            for idx, length in words_dict[target[i]]:
                if i + length > n or ans[i] + costs[idx] >= ans[i + length]:
                    continue
                if get_hash(i, i + length) == words[idx]:
                    ans[i + length] = ans[i] + costs[idx]

        return ans[-1] if ans[-1] < float("inf") else -1
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