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

const int N = 1e4+5, M = 105, MOD = (int)1e9+7;
string k;
int d, dp[N][M][2];

int solve(int idx, int rem, int less){
    int &res = dp[idx][rem][less];
    if(idx == k.size())
        return rem == 0;
    if(res != -1)
        return res;
    res = 0;
    for(int i = 0; i <= ((less)? 9 : (int)(k[idx] - '0')); ++i){
        res += solve(idx + 1, (rem + i) % d, less | (k[idx] - '0') > i);
        res %= MOD;
    }
    return res;
}

int main(){
    cin >> k >> d;
    int n = k.size();
    memset(dp, -1, sizeof(dp));
    cout << (solve(0, 0, 0) - 1 + MOD) % MOD;
}

### Prompt

Please create a solution in Cpp 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, M = 105, MOD = (int)1e9+7;
string k;
int d, dp[N][M][2];

int solve(int idx, int rem, int less){
    int &res = dp[idx][rem][less];
    if(idx == k.size())
        return rem == 0;
    if(res != -1)
        return res;
    res = 0;
    for(int i = 0; i <= ((less)? 9 : (int)(k[idx] - '0')); ++i){
        res += solve(idx + 1, (rem + i) % d, less | (k[idx] - '0') > i);
        res %= MOD;
    }
    return res;
}

int main(){
    cin >> k >> d;
    int n = k.size();
    memset(dp, -1, sizeof(dp));
    cout << (solve(0, 0, 0) - 1 + MOD) % MOD;
}

```