<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 {
    const int mod=1e9+7;
    int f(int i, int j, string& s, int k, vector<int>& dp){
        if(dp[i]!=-1)
            return dp[i];
        if(i>j)
            return dp[i]=0;
        if(s[i]=='0')
            return 0;
        long long res=0;
        for(int idx=i;idx<=j;idx++){
            // if(idx-i+1>10)break;
            long long x=stoll(s.substr(i,idx-i+1));
            if(x>k)break;
            res+=(idx==j)?1:f(idx+1,j,s,k,dp);
            res%=mod;
        }
        return dp[i]=res;
    }
public:
    int numberOfArrays(string& s, int k) {
        int n=s.size();
        // vector<int> dp(n+1,-1);
        // return f(0,n-1,s,k,dp);
        vector<int> dp(n+1,0);
        for(int i=n-1;i>=0;i--){
            if(s[i]=='0')
                continue;
            long long res=0;
            for(int idx=i;idx<n;idx++){
                // if(idx-i+1>10)break;
                long long x=stoll(s.substr(i,idx-i+1));
                if(x>k)break;
                res+=(idx==n-1)?1:dp[idx+1];
                res%=mod;
            }
            dp[i]=res;
        }
        return dp[0];
    }
};
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