<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 {
private:
    int mod = 1e9+7;
    int call(int index, string &s, int &k, vector<int> &dp){
        if(index >= s.length()) return 1;
        if(s[index] - 48 == 0) return 0;
        int ans = 0;

        if(dp[index] != -1) return dp[index];

        long long num = 0;
        for(int i=index ; i<s.length() && (i-index)<10 ; i++){
            // if((i-index) == 9 && s[index] - 48 > 1) break;
            // long long num = stoll(s.substr(index, i-index+1));
             num = num*10 + (s[i]-'0');
            
            if(num > k) break;
            ans = (ans + call(i+1, s, k, dp))%mod;
        }

        return dp[index] = ans;
    }

public:
    int numberOfArrays(string s, int k) {
        int index = 0;
        vector<int> dp(s.length()+1, -1);
        return call(index, s, k, dp);
    }
};
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