<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 dfs(self, idx, digit_sum, tight, num, min_sum, max_sum, memo):
        MOD = int(1e9 + 7)
        if idx == len(num):
            return 1 if min_sum <= digit_sum <= max_sum else 0
        if (idx, digit_sum, tight) in memo:
            return memo[(idx, digit_sum, tight)]
        limit = ord(num[idx]) - ord('0') if tight else 9
        res = 0
        for i in range(limit + 1):
            new_tight = tight and i == limit
            res += self.dfs(idx + 1, digit_sum + i, new_tight, num, min_sum, max_sum, memo)
            # res %= MOD
        memo[(idx, digit_sum, tight)] = res
        return res


    def count(self, num1: str, num2: str, min_sum: int, max_sum: int) -> int:
        MOD = int(1e9 + 7)
        memo = {}  # (idx, digit_sum, tight): cnt;
        # until idx, the solution for whose digits' sum is digit_sum and tight is tight

        num1 = str(int(num1) - 1)
        tight = True
        r1 = self.dfs(0, 0, tight, num1, min_sum, max_sum, memo)
        print(r1)
        memo = {}
        r2 = self.dfs(0, 0, tight, num2, min_sum, max_sum, memo)
        print(r2)
        return (r2 - r1) % MOD
434