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
func possibleStringCount(word string, k int) int {
	const mod = 1_000_000_007
	nums := []int{}
	ans := 1
	cur := 0
	n := len(word)

	for i := 0; i < n; i++ {
		cur++
		if i == n-1 || word[i] != word[i+1] {
			if cur > 1 {
				if k > 0 {
					nums = append(nums, cur-1)
				}
				ans = ans * cur % mod
			}
			cur = 0
			k--
		}
	}

	if k < 1 {
		return ans
	}

	m := len(nums)
	f := make([][]int, m+1)
	for i := range f {
		f[i] = make([]int, k)
	}
	f[0][0] = 1

	for i := 1; i <= m; i++ {
		x := nums[i-1]
		s := make([]int, k+1)
		for j := 0; j < k; j++ {
			s[j+1] = (s[j] + f[i-1][j]) % mod
		}
		for j := 0; j < k; j++ {
			l := j - x
			if l < 0 {
				l = 0
			}
			f[i][j] = (s[j+1] - s[l] + mod) % mod
		}
	}

	sum := 0
	for j := 0; j < k; j++ {
		sum = (sum + f[m][j]) % mod
	}

	return (ans - sum + mod) % mod
}
