<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 n;
    // if next is 0 don't break rn
    // if including the next will make it greater than k then break it
    vector<int> dp;
    int k;
    string s;
    long long int f(long long int indx) {
        if (indx == n)
            return 1;
        long long int ans = 0;
        auto &x = dp[indx];
        if(x!=-1) return x;
        long long int curr = 0;
        for (long long int i = indx; i < n; i++) {
            curr = curr * 10 + (s[i] - '0');
            if(curr > k )
            {
                break;
            }
            if (indx == n - 1) {
                ans += f(i + 1)%m;
                break;
            } else if (curr <= k and s[i + 1] != '0') {
                ans += f(i + 1)%m;
            }
        }
        return x = ans%m;
    }
    int numberOfArrays(string s, int k) {
        n = s.size();
        this->s = s;
        this->k = k;
        dp.assign(n, -1);
        return f(0)%m;
    }
};
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