Problem: Assume that sk(n) equals the sum of digits of number n in the k-based notation. For example, s2(5) = s2(1012) = 1 + 0 + 1 = 2, s3(14) = s3(1123) = 1 + 1 + 2 = 4.

The sequence of integers a0, ..., an - 1 is defined as <image>. Your task is to calculate the number of distinct subsequences of sequence a0, ..., an - 1. Calculate the answer modulo 109 + 7.

Sequence a1, ..., ak is called to be a subsequence of sequence b1, ..., bl, if there is a sequence of indices 1 ≤ i1 < ... < ik ≤ l, such that a1 = bi1, ..., ak = bik. In particular, an empty sequence (i.e. the sequence consisting of zero elements) is a subsequence of any sequence.

Input

The first line contains two space-separated numbers n and k (1 ≤ n ≤ 1018, 2 ≤ k ≤ 30).

Output

In a single line print the answer to the problem modulo 109 + 7.

Examples

Input

4 2


Output

11


Input

7 7


Output

128

Note

In the first sample the sequence ai looks as follows: (0, 1, 1, 0). All the possible subsequences are: 

(), (0), (0, 0), (0, 1), (0, 1, 0), (0, 1, 1), (0, 1, 1, 0), (1), (1, 0), (1, 1), (1, 1, 0).

In the second sample the sequence ai looks as follows: (0, 1, 2, 3, 4, 5, 6). The subsequences of this sequence are exactly all increasing sequences formed from numbers from 0 to 6. It is easy to see that there are 27 = 128 such sequences.

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const int mo = 1000000007;
int q[65], k;
long long n;
struct Mat {
  int a[32][32];
  Mat() { memset(a, 0, sizeof(a)); }
  Mat operator*(const Mat &b) const {
    Mat c;
    for (int i = (int)(0); i <= (int)(::k); i++)
      for (int j = (int)(0); j <= (int)(::k); j++)
        for (int k = (int)(0); k <= (int)(::k); k++)
          c.a[i][k] = (c.a[i][k] + 1ll * a[i][j] * b.a[j][k]) % mo;
    return c;
  }
};
Mat pre[32], suf[32];
Mat f[65][32], ans;
int main() {
  scanf("%lld%d", &n, &k);
  ans.a[0][k] = 1;
  for (; n; n /= k) q[++*q] = n % k;
  for (int i = (int)(0); i <= (int)(k - 1); i++)
    for (int j = (int)(0); j <= (int)(k); j++)
      f[1][i].a[j][i] = f[1][i].a[j][j] = 1;
  for (int i = (int)(2); i <= (int)(*q); i++) {
    pre[0] = f[i - 1][0];
    suf[k - 1] = f[i - 1][k - 1];
    for (int j = (int)(1); j <= (int)(k - 1); j++)
      pre[j] = pre[j - 1] * f[i - 1][j];
    for (int j = (int)(k - 2); j >= (int)(0); j--)
      suf[j] = f[i - 1][j] * suf[j + 1];
    f[i][0] = suf[0];
    for (int j = (int)(1); j <= (int)(k - 1); j++)
      f[i][j] = suf[j] * pre[j - 1];
  }
  int sum = 0;
  for (int i = (int)(*q); i >= (int)(1); i--) {
    for (int j = (int)(0); j <= (int)(q[i] - 1); j++)
      ans = ans * f[i][(sum + j) % k];
    sum = (sum + q[i]) % mo;
  }
  sum = 0;
  for (int i = (int)(0); i <= (int)(k); i++)
    sum = (sum + 1ll * ans.a[0][i]) % mo;
  printf("%d\n", sum);
}