<p>A program was supposed to print an array of integers. The program forgot to print whitespaces and the array is printed as a string of digits <code>s</code> and all we know is that all integers in the array were in the range <code>[1, k]</code> and there are no leading zeros in the array.</p>

<p>Given the string <code>s</code> and the integer <code>k</code>, return <em>the number of the possible arrays that can be printed as </em><code>s</code><em> using the mentioned program</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;1000&quot;, k = 10000
<strong>Output:</strong> 1
<strong>Explanation:</strong> The only possible array is [1000]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;1000&quot;, k = 10
<strong>Output:</strong> 0
<strong>Explanation:</strong> There cannot be an array that was printed this way and has all integer &gt;= 1 and &lt;= 10.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;1317&quot;, k = 2000
<strong>Output:</strong> 8
<strong>Explanation:</strong> Possible arrays are [1317],[131,7],[13,17],[1,317],[13,1,7],[1,31,7],[1,3,17],[1,3,1,7]
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>s</code> consists of only digits and does not contain leading zeros.</li>
	<li><code>1 &lt;= k &lt;= 10<sup>9</sup></code></li>
</ul>

class Solution:
    def __init__(self):
        self.cache = {}

    def memoize(func):
        def wrapper(self, s, k, indx):
            if (indx, k) not in self.cache:
                self.cache[(indx, k)] = func(self, s, k, indx)
            return self.cache[(indx, k)]

        return wrapper

    @memoize
    def helper(self, s, k, indx):
        if indx >= len(s):
            return 0

        num_arr = 0
        i = indx + 1
        # for i in range(1, len(s) + 1):
        while i <= len(s):
            tmp = int(s[indx:i])
            if tmp > k:
                break
            elif tmp <= k and s[i:] and s[i] != "0":
                num_arr += self.helper(s, k, i)
            elif tmp <= k and s[i:] == "":
                num_arr += 1
                break

            i += 1

        return num_arr % (7 + 10**9)

    def numberOfArrays(self, s: str, k: int) -> int:
        return self.helper(s, k, 0)
        # if not s:
        #     return 0

        # num_arr = 0
        # for i in range(1, len(s) + 1):
        #     tmp = int(s[:i])
        #     if tmp > k:
        #         break
        #     elif tmp <= k and s[i:] and s[i] != "0":
        #         num_arr += self.numberOfArrays(s[i:], k)
        #     elif tmp <= k and s[i:] == "":
        #         num_arr += 1
        #         break

        # return num_arr % (7 + 10**9)

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