<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 c = 0;
    int mod = 1e9 + 7;
    long long dp[100100];
    long long rec(int level,string& s,int& k){
        //pruning and base case
        if(level == s.size()){
            return 1;
        }

        if(s[level] == '0'){
            return 0;
        }

        //cache check
        if(dp[level] != -1){
            return dp[level];
        }

        //transitions
        long long ans = 0;
        long long y = 0;
        for(int i = level;i < s.size();i++){
                y = y*10 + (s[i]-'0');
                if(y > k){
                    break;
                }
                ans = ans + rec(i+1,s,k)%mod;
                ans = ans%mod;
        }
        
        //save and return
        return dp[level] = ans%mod;
    }
    int numberOfArrays(string s, int k) {
       int x = k;
       while(x != 0){
        c++;
        x = x/10;
       } 

       memset(dp,-1,sizeof(dp));
       long long p = rec(0,s,k)%mod;

       return p;

    }
};
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