Reziba has many magic gems. Each magic gem can be split into M normal gems. The amount of space each magic (and normal) gem takes is 1 unit. A normal gem cannot be split.

Reziba wants to choose a set of magic gems and split some of them, so the total space occupied by the resulting set of gems is N units. If a magic gem is chosen and split, it takes M units of space (since it is split into M gems); if a magic gem is not split, it takes 1 unit.

How many different configurations of the resulting set of gems can Reziba have, such that the total amount of space taken is N units? Print the answer modulo 1000000007 (10^9+7). Two configurations are considered different if the number of magic gems Reziba takes to form them differs, or the indices of gems Reziba has to split differ.

Input

The input contains a single line consisting of 2 integers N and M (1 ≤ N ≤ 10^{18}, 2 ≤ M ≤ 100).

Output

Print one integer, the total number of configurations of the resulting set of gems, given that the total amount of space taken is N units. Print the answer modulo 1000000007 (10^9+7).

Examples

Input


4 2


Output


5


Input


3 2


Output


3

Note

In the first example each magic gem can split into 2 normal gems, and we know that the total amount of gems are 4.

Let 1 denote a magic gem, and 0 denote a normal gem.

The total configurations you can have is: 

  * 1 1 1 1 (None of the gems split); 
  * 0 0 1 1 (First magic gem splits into 2 normal gems); 
  * 1 0 0 1 (Second magic gem splits into 2 normal gems); 
  * 1 1 0 0 (Third magic gem splits into 2 normal gems); 
  * 0 0 0 0 (First and second magic gems split into total 4 normal gems). 



Hence, answer is 5.
import java.io.*;
import java.util.InputMismatchException;

public class MagicGems {

    private static boolean LOCAL;
    static {
        try { LOCAL = "aurel".equalsIgnoreCase(System.getenv().get("USER")); } catch (Exception e){}
    }

    private static final String TEST =
        "3 2";

    void solve(InputReader in, PrintWriter out) {
        long n = in.nextLong();
        int m = in.nextInt();
        if (n < m) {
            out.println(1);
            return;
        }

        long mod = 1_000_000_007;
        long[][] a = new long[m][m];
        a[0][0] = a[0][m - 1] = 1;
        for (int i = 1; i < m; i++) {
            a[i][i - 1] = 1;
        }

        a = powMod(a, n - m + 1, mod);
        long ans = 0;
        for (int i = 0; i < m; i++) {
            ans = (ans + a[0][i]) % mod;
        }
        System.out.println(ans);
    }

    private static long[][] powMod(long[][] a, long b, long mod) {
        int n = a.length;
        long[][] p = eye(n);
        while (b > 0) {
            if (b % 2 == 1) {
                p = mul(p, a, mod);
            }
            a = mul(a, a, mod);
            b /= 2;
        }
        return p;
    }

    private static long[][] mul(long[][] a, long[][] b, long mod) {
        int n = a.length;
        long[][] c = new long[n][n];
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                for (int k = 0; k < n; k++) {
                    c[i][j] = (c[i][j] + a[i][k] * b[k][j]) % mod;
                }
            }
        }
        return c;
    }

    private static long[][] eye(int n) {
        long[][] a = new long[n][n];
        for (int i = 0; i < n; i++) {
            a[i][i] = 1;
        }
        return a;
    }

    //region main
    public static void main(String[] args) throws Exception {
        long t = System.currentTimeMillis();

        try (
            InputReader in = new StreamInputReader(!LOCAL ? System.in : new ByteArrayInputStream(TEST.getBytes()));
            PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out, 2048), false)
        ) {
            new MagicGems().solve(in, out);
        }

        System.err.println("time: " + (System.currentTimeMillis() - t) + "ms");
    }
    //endregion

    //region fast io
    abstract static class InputReader implements AutoCloseable {

        public abstract int read();

        public int nextInt() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String next() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }

    static class StreamInputReader extends InputReader {

        private InputStream stream;
        private byte[] buf;
        private int curChar, numChars;

        public StreamInputReader(InputStream stream) {
            this(stream, 2048);
        }

        public StreamInputReader(InputStream stream, int bufSize) {
            this.stream = stream;
            this.buf = new byte[bufSize];
        }

        @Override
        public int read() {
            if (numChars == -1) {
                throw new InputMismatchException();
            }
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) {
                    return -1;
                }
            }
            return buf[curChar++];
        }

        @Override
        public void close() throws Exception {
            stream.close();
        }

    }
    //endregion

    //region imports
    //endregion

}
