<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 {
    typedef long long LL;
public:
    int numberOfArrays(string s, int k) {
        const int MOD = 1e9 + 7;
        int N = s.size();
        
        // Edge case: if the first character is greater than k, return 0
        if (s[0] - '0' > k) return 0;

        // Calculate the maximum number of digits in k
        int maxDigits = 0, temp = k;
        while (temp) {
            temp /= 10;
            ++maxDigits;
        }

        vector<int> dp(N + 1, 0);
        dp[0] = 1; // Base case: empty array
        
        for (int i = 1; i <= N; ++i) {
            LL num = 0; // The number being formed
            LL powerOfTen = 1; // To handle digit places

            for (int j = i - 1; j >= 0; --j) {
                num += (s[j] - '0') * powerOfTen;
                powerOfTen *= 10;

                // Break if the number exceeds k or has more digits than allowed
                if (num > k || i - j > maxDigits) break;

                // Skip invalid numbers like those with leading zeros
                if (num == 0 || s[j] == '0') continue;

                // Update dp[i] by adding the number of ways to split the substring
                dp[i] = (dp[i] + dp[j]) % MOD;
            }
        }

        return dp[N];
    }
};

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