Problem: You have a team of N people. For a particular task, you can pick any non-empty subset of people. The cost of having x people for the task is xk. 

Output the sum of costs over all non-empty subsets of people.

Input

Only line of input contains two integers N (1 ≤ N ≤ 109) representing total number of people and k (1 ≤ k ≤ 5000).

Output

Output the sum of costs for all non empty subsets modulo 109 + 7.

Examples

Input

1 1


Output

1


Input

3 2


Output

24

Note

In the first example, there is only one non-empty subset {1} with cost 11 = 1.

In the second example, there are seven non-empty subsets.

- {1} with cost 12 = 1

- {2} with cost 12 = 1

- {1, 2} with cost 22 = 4

- {3} with cost 12 = 1

- {1, 3} with cost 22 = 4

- {2, 3} with cost 22 = 4

- {1, 2, 3} with cost 32 = 9

The total cost is 1 + 1 + 4 + 1 + 4 + 4 + 9 = 24.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class MainG
{

    static int mod = (int) (1e9+7);
    static InputReader in;
    static PrintWriter out;

    static long[][] nCr;

    static void choose(int maxN, int maxR) {
        nCr = new long[maxN + 1][maxR + 1];
        for (int i = 0; i <= maxN; i++) {
            for (int j = 0; j <= i; j++) {
                if (j == 0 || j == i || i == 0) {
                    nCr[i][j] = 1;
                } else {
                    nCr[i][j] = (nCr[i - 1][j - 1] + nCr[i - 1][j]) % mod;
                }
            }
        }
    }

    static long nCr(int n, int r) {
        if (n == r) {
            return 1;
        }
        if (n < 0 || r < 0) {
            return 0;
        }
        return nCr[n][r];
    }
    
    static long[][] dp;
    static int n;
    
    static long solve(int i, int k){
        if(k == 1) return i * pow(2, i - 1, mod);
        if(dp[n - i][k] != -1) return dp[n - i][k];
        long res = (solve(i, k - 1)) % mod;
        res = (res - solve(i - 1, k - 1) + mod) % mod;
        res = (res * i) % mod;
        return dp[n - i][k] = res;
    }

    static void solve()
    {
        in = new InputReader(System.in);
        out = new PrintWriter(System.out);            
        
        n = in.nextInt();
        int k = in.nextInt();
        
        if(n <= k){
            choose(k, k);
            long res = 0;
            for(int i = 1; i <= n; i++){
                res = (res + (nCr(n, i) * pow(i, k, mod)) % mod) % mod;
            }
            out.println(res);
        }
        else{
            dp = new long[k + 1][k + 1];
            for(int i = 0; i <= k; i++)
                Arrays.fill(dp[i], -1);
            out.println(solve(n, k));
        }
        out.close();
        
    }
    
    public static void main(String[] args)
    {
        new Thread(null ,new Runnable(){
            public void run()
            {
                try{
                    solve();
                } catch(Exception e){
                    e.printStackTrace();
                }
            }
        },"1",1<<26).start();

    }
    
    static void debug(Object... o)
    {
            System.out.println(Arrays.deepToString(o));
    }

    static class Pair implements Comparable<Pair>
    {

        int x,y,i;
        
        Pair (int x, int y,int i)
        {
		this.x = x;
                this.y = y;
                this.i = i;
	}
	
	public int compareTo(Pair o) {
                return -Integer.compare(this.y,o.y);
	}

        public boolean equals(Object o)
        {
            if (o instanceof Pair)
            {
                Pair p = (Pair)o;
                return p.x == x && p.y==y;
            }
            return false;
        }

        @Override
        public String toString()
        {
            return x + " "+ y;
        }
        
        public int hashCode()
        {
            return new Long(x).hashCode() * 31 + new Long(y).hashCode();
        }
    
    } 

    static long add(long a,long b){
        long x=(a+b);
        while(x>=mod) x-=mod;
        return x;
    }

    static long sub(long a,long b){
        long x=(a-b);
        while(x<0) x+=mod;
        return x;
    }
    
    static long mul(long a,long b){
        long x=(a*b);
        while(x>=mod) x-=mod;
        return x;
    }
    
    static String rev(String s){
        StringBuilder sb=new StringBuilder(s);
        sb.reverse();
        return sb.toString();
    }
    
    static long gcd(long x,long y)
    {
        if(y==0)
                return x;
        else
                return gcd(y,x%y);
    }

    static int gcd(int x,int y)
    {
        if(y==0)
                return x;
        else 
                return gcd(y,x%y);
    }

    static long pow(long n,long p,long m)
    {
         long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result>=m)
            result%=m;
            p >>=1;
            n*=n;
            if(n>=m)
            n%=m;
        }
        return result;
    }

    static long pow(long n,long p)
    {
        long  result = 1;
          if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;	    
            p >>=1;
            n*=n;	    
        }
        return result;
    }

    static class InputReader
    {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;
        private SpaceCharFilter filter;

        public InputReader(InputStream stream)
        {
                this.stream = stream;
        }

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

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

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

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

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

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

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

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

        private boolean isEndOfLine(int c)
        {
                return c == '\n' || c == '\r' || c == -1;
        }

        public interface SpaceCharFilter
        {
                public boolean isSpaceChar(int ch);
        }

    }
}