#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    const int mod=1000000007;
    string k;
    int d;
    cin >> k >> d;
    int n=k.size();
    vector<int> now(d,0);
    int val=0;
    for(int i=0;i<n;i++)
    {
        vector<int> nxt(d,0);
        int x=(k[i]-'0');
        for(int a=0;a<x;a++) nxt[(val+a)%d]=(nxt[(val+a)%d]+1)%mod;
        val=(val+x)%d;
        for(int j=0;j<d;j++)
        {
            for(int a=0;a<=9;a++) nxt[(j+a)%d]=(nxt[(j+a)%d]+now[j])%mod;
        }
        now=nxt;
    }
    cout << (now[0]+(val==0)-1+mod)%mod << "\n";
    return 0;
}

### Prompt

Please formulate a cpp solution to the following problem:

Find the number of integers between 1 and K (inclusive) satisfying the following condition, modulo 10^9 + 7:

* The sum of the digits in base ten is a multiple of D.

Constraints

* All values in input are integers.
* 1 \leq K < 10^{10000}
* 1 \leq D \leq 100

Input

Input is given from Standard Input in the following format:


K
D


Output

Print the number of integers satisfying the condition, modulo 10^9 + 7.

Examples

Input

30
4


Output

6


Input

1000000009
1


Output

2


Input

98765432109876543210
58


Output

635270834

### Response

```cpp
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;

int main()
{
    ios::sync_with_stdio(0);
    cin.tie(0);
    const int mod=1000000007;
    string k;
    int d;
    cin >> k >> d;
    int n=k.size();
    vector<int> now(d,0);
    int val=0;
    for(int i=0;i<n;i++)
    {
        vector<int> nxt(d,0);
        int x=(k[i]-'0');
        for(int a=0;a<x;a++) nxt[(val+a)%d]=(nxt[(val+a)%d]+1)%mod;
        val=(val+x)%d;
        for(int j=0;j<d;j++)
        {
            for(int a=0;a<=9;a++) nxt[(j+a)%d]=(nxt[(j+a)%d]+now[j])%mod;
        }
        now=nxt;
    }
    cout << (now[0]+(val==0)-1+mod)%mod << "\n";
    return 0;
}

```