<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 mod=1e9+7;
    int n;
    int v[1000001];

    int solve(int i, string&s, int &k)
    {
        if( i >= n)
        {
            return 1;
        }

        if(v[i] != -1)
        {
            return v[i];

        }

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

        long long ans=0;
        long long num=0;

        for(int j=i;j<n;++j)
        {
           /*smart way to  find sub_string without using s.substr() STL function which require 0(n) time complexity
            instead of we can use the following technique  to find out the substring in o(1) time complexity */
            num=(num*10) + (s[j]-'0');

            // if the num has already out of the range k , then no need to procced further

            if( num > k)
            {
                break;
            }

            ans=(ans%mod + solve(j+1,s,k)%mod)%mod;

        }

        return v[i]=ans;
    }
    int numberOfArrays(string s, int k) {
        n=s.size();
        memset(v,-1,sizeof(v));

        return solve(0,s,k);


        
    }
};
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