<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>

#define mod 1000000007
class Solution {
public:
    int rec(int n,int k,string &s,vector<int>&dp)
    {
        int ans = 0,sz =s.size();
        if(n==(sz+1))
            return 1;
        if(dp[n]!=-1)
            return dp[n];
        long long temp = 0;
        for(int i=n;i<=sz;i++)
        {
            temp = temp*10 + (int)(s[i-1]-'0');
            if(i<sz && s[i]=='0')
            {
                i++;
                while(i<=sz && s[i-1]=='0')
                {
                    temp*=10;
                    i++;
                }
                i--;
            }
            if(temp<=(long long)k)
            {
                ans = (ans%mod + rec(i+1,k,s,dp)%mod)%mod;
            }
            else
            {
                break;
            }
        }
        return dp[n] = ans;
    }

    int numberOfArrays(string s, int k) 
    {
        int n = s.size();
        int mx = 0;
        for(int i=0;i<n;i++)
        {
            if(s[i]=='0')
            {
                int cnt = 0;
                while(i<n && s[i]=='0')
                {
                    cnt++;
                    i++;
                }
                i--;
                mx = max(cnt,mx);
            }
        }
        if(mx>9)
            return 0;
        vector<int>dp(n+2,-1);
        return rec(1,k,s,dp);
    }
};
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