<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>

typedef long long ll;
using vi = vector<int>;
class Solution {
public:
    int n;
    int k;

    int mod = 1e9 + 7;

    bool valid(string &str, ll k){
        // cout<<str<<" "<<(stoi(str) <= k)<<"\n";
        return (stol(str) <= k);
    }


    int numberOfArrays(string s, int _k) {

        this->n = s.length();
        this->k = _k;

        vi dp(n+1, 0);
        dp[n] = 1;

        for(int i=n-1; i>=0; i--){
            if(s[i] == '0') continue;

            string temp = "";
            
            for(int t=0; t<=10 && i+t<n; t++){

                temp += s[i+t];

                if(valid(temp, (ll)k)) dp[i] = (int)( ((ll)dp[i] % mod + (ll)dp[i + t + 1] % mod) % mod);

            }
        }

        // for(auto e: dp) cout<<e<<" ";

        return dp[0];
        
    }
};
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