#include<bits/stdc++.h>
using namespace std;
const int N=1e4+5;
const int M=105;
const int MOD=1e9+7;

int n,m;
char a[N];
int dp[2][N][M];
void Add(int &x,int y)
{
	x+=y;
	if(x>=MOD) x-=MOD;
}

int main()
{
	
	scanf("%s%d",&a,&m);
	while(a[n]!='\0') n++;
	for(int i=0;i<n;i++)
		a[i]-='0';
	
	dp[1][0][0]=1;
	for(int i=0;i<n;i++)
	for(int j=0;j<m;j++)
	for(int k=0;k<10;k++)
	{
		Add(dp[0][i+1][(j+k)%m],dp[0][i][j]);
		if(k>a[i]) continue;
		if(k==a[i]) Add(dp[1][i+1][(j+k)%m],dp[1][i][j]);
		else Add(dp[0][i+1][(j+k)%m],dp[1][i][j]);
	}
	printf("%d\n",(dp[0][n][0]+dp[1][n][0]-1+MOD)%MOD);
	
	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;
const int N=1e4+5;
const int M=105;
const int MOD=1e9+7;

int n,m;
char a[N];
int dp[2][N][M];
void Add(int &x,int y)
{
	x+=y;
	if(x>=MOD) x-=MOD;
}

int main()
{
	
	scanf("%s%d",&a,&m);
	while(a[n]!='\0') n++;
	for(int i=0;i<n;i++)
		a[i]-='0';
	
	dp[1][0][0]=1;
	for(int i=0;i<n;i++)
	for(int j=0;j<m;j++)
	for(int k=0;k<10;k++)
	{
		Add(dp[0][i+1][(j+k)%m],dp[0][i][j]);
		if(k>a[i]) continue;
		if(k==a[i]) Add(dp[1][i+1][(j+k)%m],dp[1][i][j]);
		else Add(dp[0][i+1][(j+k)%m],dp[1][i][j]);
	}
	printf("%d\n",(dp[0][n][0]+dp[1][n][0]-1+MOD)%MOD);
	
	return 0;
}
```