<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>

#include <vector>
#include <string>

class Solution {
public:
    const int M = 1000000007;

    int solve(const string& s, int k, int index,vector<int>& dp) {
        int n = s.length();
        if (index == n) return 1;
        if (s[index] == '0') return 0;
        if (dp[index] != -1) return dp[index];
        
        int ans = 0;
        long long num = 0;
        for (int i = index; i < n; ++i) {
            num = (num * 10) + (s[i] - '0');
            if (num >= 1 && num <= k) {
                ans = (ans + solve(s, k, i + 1, dp)) % M;
            } else {
                break;
            }
        }
        return dp[index] = ans;
    }

    int numberOfArrays(const std::string& s, int k) {
        int n = s.length();
        std::vector<int> dp(n, -1);
        return solve(s, k, 0, dp);
    }
};

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