<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 {
public:
int n;
int mod = 1e9 + 7;
int dp[1000001];
int solve(string &s, int start, int k) {
    if (start >= n) {
        return 1;
    }
    if (s[start] == '0') {
        return 0;  // Leading zeros are invalid
    }
    if(dp[start]!=-1){
        return dp[start];
    }
    int ans = 0;
    long num = 0;
    for (int end = start; end < n; ++end) {
        num = num * 10 + (s[end] - '0');  // Convert substring to number
        if (num > k) {
            break;  // If the number exceeds k, stop further recursion
        }
        ans = (ans + solve(s, end + 1, k)) % mod;  // Recurse for the next substring
    }
    return dp[start]=ans;
}

int numberOfArrays(string s, int k) {
    memset(dp,-1,sizeof(dp));
    n = s.length();
    return solve(s, 0, k);
}
};
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