<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:
        if min_sum > len(num2) * 9: return 0

        num1 = str(int(num1) - 1)
        min_sum -= 1
        v = sb(num2, max_sum) - sb(num2, min_sum) - sb(num1, max_sum) + sb(num1, min_sum)
        return v % int(1e9 + 7)

# sum below
def sb(num, sum):
    return count_x(len(num), sum, num)

@cache
def count_9(n_digits, max_sum):
    if max_sum < 0: return 0
    if n_digits == 1: return min(9, max_sum) + 1
    c = 0
    for i in range(10):
        c += count_9(n_digits - 1, max_sum - i)
    return c

def count_x(n_digits, max_sum, num):
    if max_sum < 0: return 0
    x = int(num[-n_digits])
    if n_digits == 1: return min(x, max_sum) + 1
    c = count_x(n_digits - 1, max_sum - x, num)
    for i in range(x):
        c += count_9(n_digits - 1, max_sum - i)
    return c
60