<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 n;
int dp[100001];
 const int mod = 1e9+7;
    int solve(int ind,string &s,int k){
        if(ind==n) return 1;

        if(s[ind]=='0') return 0;
        if(dp[ind]!=-1) return dp[ind];

        int ways=0;
        long long num=0;

        for(int i=ind;i<n;i++){
            num = num * 10 + (s[i] - '0');  // Construct the number incrementally
            if (num > k) break; 
        ways=(ways+solve(i+1,s,k))%mod;
        }
        return dp[ind]=ways;
    }
    int numberOfArrays(string s, int k) {
        memset(dp,-1,sizeof(dp));
        n=s.size();
        return solve(0,s,k);
    }
};
20016