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.Arrays;
import java.util.StringJoiner;
import java.util.StringTokenizer;
import java.util.function.IntBinaryOperator;

public class Main {

    static long N;
    static int M;

    public static void main(String[] args) {
        FastScanner sc = new FastScanner(System.in);
        N = sc.nextLong();
        M = sc.nextInt();

        System.out.println(solve());
    }

    static int MOD = 1_000_000_007;

    static int solve() {
        // 右側に 0* or 1 をくっつけていくDPを考える
        // M=3のケース
        // f4 = f1 + f3
        // f3 = f2
        // f2 = f1
        IntMat mat = new IntMat(M, M);
        mat.set(0, 0, 1);
        mat.set(0, M-1, 1);
        for (int i = 1; i < M; i++) {
            mat.set(i, i-1, 1);
        }

        IntMat powed = IntMat.pow(mat, N, MOD);
        IntMat in = new IntMat(M, 1);
        in.set(0, 0, 1);
        IntMat out = IntMat.dot(powed, in, MOD);
        return out.get(0, 0);
    }

    static class IntMat {

        final int[][] mat;

        IntMat(int r, int c) {
            mat = new int[r][c];
        }

        IntMat(int[][] mat) {
            this.mat = mat;
        }

        IntMat(int[] vec) {
            mat = new int[vec.length][1];
            for (int i = 0; i < vec.length; i++) {
                mat[i][0] = vec[i];
            }
        }

        static IntMat pow(IntMat m, long k, int mod) {
            if( m.row() != m.col() ) throw new IllegalArgumentException("row != col : " + m.row() + " " + m.col());

            int n = m.row();
            IntMat ret = new IntMat(n, n);
            for (int i = 0; i < n; i++) {
                ret.set(i, i, 1);
            }
            if( k == 0 ) return ret; // どうだろ...

            while( k > 0 ) {
                if( (k & 1) == 1 ) {
                    ret = IntMat.dot(ret, m, mod);
                }

                m = IntMat.dot(m, m, mod);
                k = k >> 1L;
            }
            return ret;
        }

        static IntMat pow(IntMat m, long k, IntBinaryOperator mul, IntBinaryOperator add) {
            if( m.row() != m.col() ) throw new IllegalArgumentException("row != col : " + m.row() + " " + m.col());

            int n = m.row();
            IntMat ret = new IntMat(n, n);
            for (int i = 0; i < n; i++) {
                ret.set(i, i, 1);
            }
            if( k == 0 ) return ret; // どうだろ...

            while( k > 0 ) {
                if( (k & 1) == 1 ) {
                    ret = IntMat.dot(ret, m, mul, add);
                }

                m = IntMat.dot(m, m, mul, add);
                k = k >> 1L;
            }
            return ret;
        }

        static IntMat dot(IntMat a, IntMat b) {
            return dot(a, b, (i, j) -> i*j, (i, j) -> i+j);
        }

        static IntMat dot(IntMat a, IntMat b, IntBinaryOperator mul, IntBinaryOperator add) {
            int[][] ret = new int[a.row()][b.col()];

            for (int r = 0; r < a.row(); r++) {
                for (int c = 0; c < b.col(); c++) {
                    int sum = 0;
                    for (int i = 0; i < b.row(); i++) {
                        sum = add.applyAsInt(sum, mul.applyAsInt(a.get(r, i), b.get(i, c)));
                    }
                    ret[r][c] = sum;
                }
            }
            return new IntMat(ret);
        }

        static IntMat dot(IntMat a, IntMat b, int mod) {
            long m2 = (long)mod * mod;

            int ar = a.row();
            int bc = b.col();
            int br = b.row();
            int[][] ret = new int[ar][bc];

            for (int r = 0; r < ar; r++) {
                for (int c = 0; c < bc; c++) {
                    long sum = 0;
                    for (int i = 0; i < br; i++) {
                        long ab = (long)a.mat[r][i] * b.mat[i][c];
                        sum += ab;
                        if( sum >= m2 ) {
                            sum -= m2;
                        }
                    }
                    ret[r][c] = (int)(sum % mod);
                }
            }
            return new IntMat(ret);
        }

        void set(int r, int c, int n) {
            mat[r][c] = n;
        }

        int get(int r, int c) {
            try {
                return mat[r][c];
            } catch( ArrayIndexOutOfBoundsException e ) {
                throw new RuntimeException("wrong index : r=" + r + " c=" + c + " row=" + row() + " col=" + col());
            }
        }

        int row() {
            return mat.length;
        }

        int col() {
            return mat[0].length;
        }
    }

    @SuppressWarnings("unused")
    static class FastScanner {
        private BufferedReader reader;
        private StringTokenizer tokenizer;

        FastScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
            tokenizer = null;
        }

        String next() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        String nextLine() {
            if (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    return reader.readLine();
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken("\n");
        }

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

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

        int[] nextIntArray(int n) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt();
            return a;
        }

        int[] nextIntArray(int n, int delta) {
            int[] a = new int[n];
            for (int i = 0; i < n; i++) a[i] = nextInt() + delta;
            return a;
        }

        long[] nextLongArray(int n) {
            long[] a = new long[n];
            for (int i = 0; i < n; i++) a[i] = nextLong();
            return a;
        }
    }

    static void writeLines(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int a : as) pw.println(a);
        pw.flush();
    }

    static void writeLines(long[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (long a : as) pw.println(a);
        pw.flush();
    }

    static void writeSingleLine(int[] as) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < as.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(as[i]);
        }
        pw.println();
        pw.flush();
    }

    static int max(int... as) {
        int max = Integer.MIN_VALUE;
        for (int a : as) max = Math.max(a, max);
        return max;
    }

    static int min(int... as) {
        int min = Integer.MAX_VALUE;
        for (int a : as) min = Math.min(a, min);
        return min;
    }

    static void debug(Object... args) {
        StringJoiner j = new StringJoiner(" ");
        for (Object arg : args) {
            if (arg == null) j.add("null");
            else if (arg instanceof int[]) j.add(Arrays.toString((int[]) arg));
            else if (arg instanceof long[]) j.add(Arrays.toString((long[]) arg));
            else if (arg instanceof double[]) j.add(Arrays.toString((double[]) arg));
            else if (arg instanceof Object[]) j.add(Arrays.toString((Object[]) arg));
            else j.add(arg.toString());
        }
        System.err.println(j.toString());
    }

    static void printSingleLine(int[] array) {
        PrintWriter pw = new PrintWriter(System.out);
        for (int i = 0; i < array.length; i++) {
            if (i != 0) pw.print(" ");
            pw.print(array[i]);
        }
        pw.println();
        pw.flush();
    }

    static int lowerBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] < value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }

    static int upperBound(int[] array, int value) {
        int lo = 0, hi = array.length, mid;
        while (lo < hi) {
            mid = (hi + lo) / 2;
            if (array[mid] <= value) lo = mid + 1;
            else hi = mid;
        }
        return lo;
    }
}
