#include<bits/stdc++.h>
using namespace std;
#define mod 1000000007

string str;
int d;
long long dp[10005][2][101];

long long solution(int n , int tight , int mo){

if(n==str.size()){
    return (mo==0) ? 1 : 0;
}
if(dp[n][tight][mo] != -1){
    return dp[n][tight][mo];
}

int en = tight ? (str[n]-'0') : 9;

long long ret = 0;

for(int i=0 ; i<=en ; i++){
    ret = (ret + solution(n+1 , tight&(en==i) , (mo+i)%d)%mod);
}

return dp[n][tight][mo] = ret;


}


int main(){

    cin>>str>>d;
    memset(dp , -1 , sizeof(dp));
    cout<<(solution(0 , 1 , 0)-1+mod)%mod<<endl;
    
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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;
#define mod 1000000007

string str;
int d;
long long dp[10005][2][101];

long long solution(int n , int tight , int mo){

if(n==str.size()){
    return (mo==0) ? 1 : 0;
}
if(dp[n][tight][mo] != -1){
    return dp[n][tight][mo];
}

int en = tight ? (str[n]-'0') : 9;

long long ret = 0;

for(int i=0 ; i<=en ; i++){
    ret = (ret + solution(n+1 , tight&(en==i) , (mo+i)%d)%mod);
}

return dp[n][tight][mo] = ret;


}


int main(){

    cin>>str>>d;
    memset(dp , -1 , sizeof(dp));
    cout<<(solution(0 , 1 , 0)-1+mod)%mod<<endl;
    
}

```