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.lang.*;
import java.math.*;
import java.util.*;
import java.io.*;

public class Main {
    void solve() {
       long n=nl(); m=ni();
       long Mat[][]=new long[m+2][m+2];
       Mat[1][1]=1; Mat[m][1]=1;
       long f[]=new long[m+1];

       f[0]=1;
       for(int i=1;i<=m;i++){
           f[i]=f[i-1];
           if(i-m>=0) f[i]=add(f[i],f[i-m]);
       }
       if(n<=m){
           pw.println(f[(int)n]);
           return;
       }
       for(int j=2;j<=m+1;j++){
           Mat[j-1][j]=1;
       }
       Mat=pow(Mat,n-m);
        long ans=0;
        for(int i=1;i<=m+1;i++){
            ans=add(ans,mul(Mat[i][1],f[m-i+1]));
        }
        pw.println(ans);

    }
    int m;
    long [][] pow(long A[][],long x){
        if(x==0){
            long C[][]=new long[m+2][m+2];
            for(int i=1;i<=m+1;i++) C[i][i]=1;
            return C;
        }else if(x==1){
            return A;
        }
        long C[][]=pow(A,x/2);
        C=mul(C,C);
        if((x&1)>0) return mul(A,C);
        return C;

    }
    long [][] mul(long A[][],long B[][]){
        long C[][]=new long[m+2][m+2];
        for(int i=1;i<=m+1;i++){
            for(int j=1;j<=m+1;j++){
                for(int k=1;k<=m+1;k++){
                    C[i][j]=add(C[i][j],mul(A[i][k],B[k][j]));
                }
            }
        }
        return C;
    }
    long[][] modpow(long A[][], long b)
    {
        long C[][]=new long[m+2][m+2];
        for(int i=1;i<=m+1;i++) C[i][i]=1;
        while(b>0)
        {
            if((b&1)>0) C=mul(C,A);
            A=mul(A,A);
            b>>=1;
        }
        return C;
    }
    long add(long a,long b){
        a+=b;
        if(a>=M) a-=M;
        return a;
    }
    long mul(long a,long b){
        a*=b;
        if(a>=M )a%=M;
        return a;
    }

    static int randInt(int min,int max){
        Random rand=new Random();
        int randInt=rand.nextInt((max-min)+1)+min;
        return randInt;
    }

    long M = (long)1e9+7;
    InputStream is;
    PrintWriter pw;
    String INPUT = "";

    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        pw = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        solve();
        pw.flush();
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");

    }

    public static void main(String[] args) throws Exception {
        new Main().run();
    }

    private byte[] inbuf = new byte[1024];
    public int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = is.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private double nd() {
        return Double.parseDouble(ns());
    }

    private char nc() {
        return (char) skip();
    }

    private String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    private char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }

    private char[][] nm(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ns(m);
        return map;
    }

    private int[] na(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = ni();
        return a;
    }

    private int ni() {
        int num = 0, b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }

    private boolean oj = System.getProperty("ONLINE_JUDGE") != null;

    private void tr(Object... o) {
        if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
    }

}