<p>You are given two numeric strings <code>num1</code> and <code>num2</code> and two integers <code>max_sum</code> and <code>min_sum</code>. We denote an integer <code>x</code> to be <em>good</em> if:</p>

<ul>
	<li><code>num1 &lt;= x &lt;= num2</code></li>
	<li><code>min_sum &lt;= digit_sum(x) &lt;= max_sum</code>.</li>
</ul>

<p>Return <em>the number of good integers</em>. Since the answer may be large, return it modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>Note that <code>digit_sum(x)</code> denotes the sum of the digits of <code>x</code>.</p>

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

<pre>
<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;12&quot;, <code>min_sum</code> = 1, max_sum = 8
<strong>Output:</strong> 11
<strong>Explanation:</strong> There are 11 integers whose sum of digits lies between 1 and 8 are 1,2,3,4,5,6,7,8,10,11, and 12. Thus, we return 11.
</pre>

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

<pre>
<strong>Input:</strong> num1 = &quot;1&quot;, num2 = &quot;5&quot;, <code>min_sum</code> = 1, max_sum = 5
<strong>Output:</strong> 5
<strong>Explanation:</strong> The 5 integers whose sum of digits lies between 1 and 5 are 1,2,3,4, and 5. Thus, we return 5.
</pre>

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

<ul>
	<li><code>1 &lt;= num1 &lt;= num2 &lt;= 10<sup>22</sup></code></li>
	<li><code>1 &lt;= min_sum &lt;= max_sum &lt;= 400</code></li>
</ul>

class Solution:
    def count(self, num1: str, num2: str, min_sum: int, max_sum: int) -> int:
        MOD = 1_000_000_007

        def calc(num: str) -> int:
            n = len(num)
            dp = [[[0] * (max_sum + 1) for _ in range(2)] for _ in range(n + 1)]
            dp[0][1][0] = 1  # 初始状态：第一位，限制状态下，数字和为0

            for i in range(1, n + 1):
                digit = int(num[i - 1])
                for is_limit in range(2):
                    for s in range(max_sum + 1):
                        upper = digit if is_limit else 9
                        for d in range(upper + 1):
                            if s + d <= max_sum:
                                dp[i][is_limit and d == digit][s + d] += dp[i - 1][is_limit][s]
                                dp[i][is_limit and d == digit][s + d] %= MOD

            res = 0
            for s in range(min_sum, max_sum + 1):
                res += dp[n][1][s] + dp[n][0][s]
                res %= MOD

            return res

        # 将 num1 和 num2 进行处理，得到有效的范围内符合要求的整数的个数
        res1 = calc(num2)
        res2 = calc(str(int(num1) - 1))
        return (res1 - res2 + MOD) % MOD
1181