<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:
    # 1317 k = 2000
    # 1 + f(317), 13 + f(17), 131 + f(7) 1317 + f()
    def numberOfArrays(self, s: str, k: int) -> int:
        length = len(s)
        mod = 10 ** 9 + 7
        dp = [0] * (length + 1)
        dp[-1] = 1
        suffix = [0] * (length + 2)
        suffix[-2] = 1
        # dp[m] + ... + dp[n] = suffix[m] - suffix[n + 1]
        for i in range(length - 1, -1, -1):
            if s[i] == '0':
                suffix[i] = suffix[i + 1]
                continue
            res = s[i]
            count = 0
            j = i + 1
            while j < length:
                if int(res) > k:
                    break
                # count = (count + dp[j]) % mod
                res += s[j]
                j += 1
            if j == length and int(res) <= k:
                count = (count + dp[j]) % mod
            if j == length and int(res) <= k:
                dp[i] = (suffix[i + 1] - suffix[j + 1]) % mod
            else:
                dp[i] = (suffix[i + 1] - suffix[j]) % mod
            suffix[i] = (suffix[i + 1] + dp[i]) % mod
        return dp[0]

        # memo = {}
        # def dfs(currIdx):
        #     if currIdx == length:
        #         return 1
        #     if s[currIdx] == '0':
        #         return 0
        #     if currIdx in memo:
        #         return memo[currIdx]
        #     count = 0
        #     res = ""
        #     for i in range(currIdx, length):
        #         res += s[i]
        #         if int(res) > k:
        #             break
        #         if int(res) < 1:
        #             continue
        #         count = (count + dfs(i + 1)) % mod
        #     memo[currIdx] = count
        #     return count
        # return dfs(0)

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