Count of Integers
<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>
Math; String; Dynamic Programming
function count(num1: string, num2: string, min_sum: number, max_sum: number): number {
    const mod = 1e9 + 7;
    const f: number[][] = Array.from({ length: 23 }, () => Array(220).fill(-1));
    let num = num2;
    const dfs = (pos: number, s: number, limit: boolean): number => {
        if (pos >= num.length) {
            return s >= min_sum && s <= max_sum ? 1 : 0;
        }
        if (!limit && f[pos][s] !== -1) {
            return f[pos][s];
        }
        let ans = 0;
        const up = limit ? +num[pos] : 9;
        for (let i = 0; i <= up; i++) {
            ans = (ans + dfs(pos + 1, s + i, limit && i === up)) % mod;
        }
        if (!limit) {
            f[pos][s] = ans;
        }
        return ans;
    };
    const a = dfs(0, 0, true);
    num = (BigInt(num1) - 1n).toString();
    f.forEach(v => v.fill(-1));
    const b = dfs(0, 0, true);
    return (a - b + mod) % mod;
}
