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;
template <class T, class U>
void ckmin(T &a, U b) {
  if (a > b) a = b;
}
template <class T, class U>
void ckmax(T &a, U b) {
  if (a < b) a = b;
}
long long N, K;
vector<int> num;
vector<vector<long long> > trans;
vector<vector<long long> > base[60][30], pref[60][30], suf[60][30];
long long ans;
vector<vector<long long> > mat_mul(vector<vector<long long> > a,
                                   vector<vector<long long> > b) {
  vector<vector<long long> > res(K + 1);
  for (auto i = (0); i < (K + 1); i++) res[i].resize(K + 1);
  for (auto i = (0); i < (K + 1); i++) {
    for (auto j = (0); j < (K + 1); j++) {
      res[i][j] = 0;
      for (auto k = (0); k < (K + 1); k++) {
        res[i][j] += a[i][k] * b[k][j];
        res[i][j] %= 1000000007;
      }
    }
  }
  return res;
}
vector<vector<long long> > shift(vector<vector<long long> > a, int x) {
  vector<vector<long long> > res(K + 1);
  for (auto i = (0); i < (K + 1); i++) res[i].resize(K + 1);
  for (auto i = (0); i < (K + 1); i++) {
    for (auto j = (0); j < (K + 1); j++) {
      if (a[i][j] == 0) continue;
      if (i == j)
        res[i][j] = a[i][j];
      else
        res[i][(j + x) % K] = a[i][j];
    }
  }
  return res;
}
int32_t main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> N >> K;
  while (N) {
    num.push_back(N % K);
    N /= K;
  }
  for (auto i = (0); i < (K); i++) {
    base[0][i].resize(K + 1);
    for (auto j = (0); j < (K + 1); j++) base[0][i][j].resize(K + 1);
    for (auto j = (0); j < (K + 1); j++) {
      base[0][i][j][j] = 1;
    }
    for (auto j = (0); j < (K + 1); j++) {
      base[0][i][j][i] = 1;
    }
  }
  for (auto i = (1); i < (((int)((num).size()))); i++) {
    pref[i - 1][0] = base[i - 1][0];
    for (auto j = (1); j < (K); j++) {
      pref[i - 1][j] = mat_mul(pref[i - 1][j - 1], base[i - 1][j]);
    }
    suf[i - 1][K - 1] = base[i - 1][K - 1];
    for (auto j = (K - 1) - 1; j >= (0); j--) {
      suf[i - 1][j] = mat_mul(base[i - 1][j], suf[i - 1][j + 1]);
    }
    base[i][0] = pref[i - 1][K - 1];
    for (auto j = (1); j < (K); j++) {
      base[i][j] = mat_mul(suf[i - 1][j], pref[i - 1][j - 1]);
    }
  }
  trans.resize(K + 1);
  for (auto i = (0); i < (K + 1); i++) trans[i].resize(K + 1);
  for (auto i = (0); i < (K + 1); i++) {
    for (auto j = (0); j < (K + 1); j++) {
      trans[i][j] = 0;
    }
    trans[i][i] = 1;
  }
  int sum = 0;
  for (auto i = (((int)((num).size()))) - 1; i >= (0); i--) {
    int x = num[i];
    for (auto j = (0); j < (x); j++) {
      trans = mat_mul(trans, base[i][sum]);
      sum++;
      if (sum >= K) sum -= K;
    }
  }
  ans = 1;
  for (auto i = (0); i < (K); i++) {
    ans += trans[K][i];
    ans %= 1000000007;
  }
  cout << ans << '\n';
  return 0;
}