<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>

mod = 10**9 + 7
import numpy as np
from numpy.polynomial.polynomial import polymul, polypow, polydiv
pl = [[1]]
for _ in range(22):
    pl.append( np.mod( polymul(pl[-1], [1] * 10).astype('int64'), mod ) )


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


        def f(num, change = 0, j =0):
            if j >= len(num):
                return 0
            tot = 0
            lead = int(num[j])
            # num = num[1:]
            if max_sum - min_sum >= 0:
                n = len(num) - j - 1
                k = 10
                p3 = pl[n]
                p2 = [1] * (max_sum-min_sum+1)
                outp = np.mod(polymul(p3, p2),mod)
                for i in range(lead):
                    max_target = max_sum - i - change
                    if len(outp) > max_target >= 0:
                        tot += int(outp[max_target])
                        tot %= mod
            tot += f(num, change+lead, j+1)
            tot %= mod
            return tot
        a = f(num2)
        a += (min_sum <= sum(map(int, num2)) <= max_sum)
        b = f(num1)
        # print(a,b)f
        return  (a-b) % mod

29500