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 JAVA):

Solution:
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.IOException;
import java.util.StringTokenizer;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
    private static final long MODULO = (long) 1e9 + 7;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        long n = in.nextLong();
        int k = in.nextInt();
        long[][][] a = new long[k][k + 1][k + 1];
        for (int i = 0; i < k; ++i) {
            long[][] mat = a[i];
            for (int j = 0; j < k; ++j) if (j != i) mat[j][j] = 1;
            mat[i][k] = 1;
            mat[k][k] = 2;
            mat[k][i] = MODULO - 1;
        }
        int sum = 0;
        for (long m = n; m > 0; m /= k) sum += m % k;
        long[][] mul = new long[k + 1][k + 1];
        for (int i = 0; i < mul.length; ++i) mul[i][i] = 1;
        while (n > 0) {
            sum -= n % k;
            for (int i = (int) (n % k - 1); i >= 0; --i) mul = multiply(mul, a[(sum + i) % k]);
            long[][][] prefix = new long[k][][];
            for (int i = 0; i < k; ++i) {
                if (i == 0) prefix[i] = a[i];
                else prefix[i] = multiply(a[i], prefix[i - 1]);
            }
            long[][][] suffix = new long[k][][];
            for (int i = k - 1; i >= 0; --i) {
                if (i == k - 1) suffix[i] = a[i];
                else suffix[i] = multiply(suffix[i + 1], a[i]);
            }
            for (int i = 0; i < k; ++i) {
                if (i == 0) a[i] = suffix[i];
                else a[i] = multiply(prefix[i - 1], suffix[i]);
            }
            n /= k;
        }
        long[][] res = new long[k + 1][1];
        res[k][0] = 1;
        res = multiply(mul, res);
        out.println(res[k][0]);
    }

    long[][] multiply(long[][] a, long[][] b) {
        int m = a.length;
        int n = a[0].length;
        int p = b[0].length;
        long[][] c = new long[m][p];
        for (int i = 0; i < m; ++i)
            for (int j = 0; j < n; ++j)
                for (int k = 0; k < p; ++k)
                    c[i][k] = (c[i][k] + a[i][j] * b[j][k]) % MODULO;
        return c;
    }
}

class InputReader {
    private final BufferedReader bufferedReader;
    private StringTokenizer stringTokenizer;

    public InputReader(InputStream inputStream) {
        this.bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        this.stringTokenizer = null;
    }

    public String next() {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            try {
                stringTokenizer = new StringTokenizer(bufferedReader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return stringTokenizer.nextToken();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

}