<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 M=1e9+7;
int dp[100001];
int f(int i,string &s,string &limit,int k1){
    int n=s.size();
if(i==n){
    return 1;
}
if(s[i]=='0'){
    return 0;
}
if(dp[i]!=-1){
    return dp[i];
}
int ans=0;
long long num=0;
for(int k=i;k<n;k++){
   num=num*10+s[k]-'0';
   if(num>k1){
    break;
   }
   ans=(ans+f(k+1,s,limit,k1))%M;
    // string s1=s.substr(i,k-i+1);
    
    // if((s1.size()<limit.size() || ((s1.size()==limit.size())&&(s1.compare(limit)<0))) && s1.size()>=1 ){
    //  ans=(ans+f(k+1,s,limit))%M;
    //  cout<<ans<<endl;

    // }
}
return dp[i]=ans;
}
    int numberOfArrays(string s, int k) {
        memset(dp,-1,sizeof(dp));
        string limit=to_string(k);
        //cout<<limit<<endl;
       return f(0,s,limit,k); 
    }
};
20198