<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:
        
        
        def helper(num, sums):
            res = 0
            s = str(num)
            res = (sum(int(c) for c in s) == sums)
            for i,c in enumerate(s):
                c = int(c)
                # 保留i之前的值，从i开始计算能有多少值
                for c2 in range(min(c, sums+1)):
                    res += split(sums - c2, len(s) - i - 1)
                sums -= c # 所以每次之前的都被保留了
            
            return res
                
        
        
        # split val v to k digits
        @lru_cache(None)
        def split(v, k):
            if v == 0: return 1
            if v > 9 * k or k == 0 or v < 0: return 0
            return sum(split(v - vv, k-1) for vv in range(10))
        
        
        res = 0
        num1 = str(int(num1)-1) 
        for x in range(min_sum,max_sum+1):
            res += helper(num2, x) - helper(num1,x)
        return res % (10 ** 9 + 7)
            
        # return sum(helper(num2, x) - helper(num1,x) for x in range(min_sum,max_sum+1))
854