<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 = 10**9 + 7

        def digit_sum(x):
            return sum(int(d) for d in str(x))

        def count_good(num):
            n = len(num)
            dp = [[[-1] * (max_sum + 1) for _ in range(2)] for _ in range(n + 1)]

            def dfs(pos, tight, sum_tight):
                if sum_tight > max_sum:
                    return 0
                if pos == n:
                    return 1 if min_sum <= sum_tight <= max_sum else 0
                if dp[pos][tight][sum_tight] != -1:
                    return dp[pos][tight][sum_tight]
                limit = int(num[pos]) if tight else 9
                ans = 0
                for d in range(limit + 1):
                    ans += dfs(pos + 1, tight and (d == limit), sum_tight + d)
                    ans %= mod
                dp[pos][tight][sum_tight] = ans
                return ans

            return dfs(0, 1, 0)

        def subtract_one(num):
            num = list(num)
            i = len(num) - 1
            while i >= 0 and num[i] == '0':
                num[i] = '9'
                i -= 1
            if i >= 0:
                num[i] = str(int(num[i]) - 1)
            return ''.join(num).lstrip('0') or '0'

        return (count_good(num2) - count_good(subtract_one(num1)) + mod) % mod
340