Find the Original Typed String II
<p>Alice is attempting to type a specific string on her computer. However, she tends to be clumsy and <strong>may</strong> press a key for too long, resulting in a character being typed <strong>multiple</strong> times.</p>

<p>You are given a string <code>word</code>, which represents the <strong>final</strong> output displayed on Alice&#39;s screen. You are also given a <strong>positive</strong> integer <code>k</code>.</p>

<p>Return the total number of <em>possible</em> original strings that Alice <em>might</em> have intended to type, if she was trying to type a string of size <strong>at least</strong> <code>k</code>.</p>

<p>Since the answer may be very 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>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">word = &quot;aabbccdd&quot;, k = 7</span></p>

<p><strong>Output:</strong> <span class="example-io">5</span></p>

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

<p>The possible strings are: <code>&quot;aabbccdd&quot;</code>, <code>&quot;aabbccd&quot;</code>, <code>&quot;aabbcdd&quot;</code>, <code>&quot;aabccdd&quot;</code>, and <code>&quot;abbccdd&quot;</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">word = &quot;aabbccdd&quot;, k = 8</span></p>

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

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

<p>The only possible string is <code>&quot;aabbccdd&quot;</code>.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">word = &quot;aaabbb&quot;, k = 3</span></p>

<p><strong>Output:</strong> <span class="example-io">8</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= word.length &lt;= 5 * 10<sup>5</sup></code></li>
	<li><code>word</code> consists only of lowercase English letters.</li>
	<li><code>1 &lt;= k &lt;= 2000</code></li>
</ul>
String; Dynamic Programming; Prefix Sum
class Solution:
    def possibleStringCount(self, word: str, k: int) -> int:
        mod = 10**9 + 7
        nums = []
        ans = 1
        cur = 0
        for i, c in enumerate(word):
            cur += 1
            if i == len(word) - 1 or c != word[i + 1]:
                if cur > 1:
                    if k > 0:
                        nums.append(cur - 1)
                    ans = ans * cur % mod
                cur = 0
                k -= 1
        if k < 1:
            return ans
        m = len(nums)
        f = [[0] * k for _ in range(m + 1)]
        f[0][0] = 1
        for i, x in enumerate(nums, 1):
            s = list(accumulate(f[i - 1], initial=0))
            for j in range(k):
                f[i][j] = (s[j + 1] - s[j - min(x, j)] + mod) % mod
        return (ans - sum(f[m][j] for j in range(k))) % mod
