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:
/* Author: Ronak Agarwal, reader part not written by me*/
import java.io.* ; import java.util.* ;
import static java.lang.Math.min ; import static java.lang.Math.max ;
import static java.lang.Math.abs ; import static java.lang.Math.log ;
import static java.lang.Math.pow ; import static java.lang.Math.sqrt ;
/* Thread is created here to increase the stack size of the java code so that recursive dfs can be performed */
public class A{
	public static void main(String[] args) throws IOException{
		new Thread(null,new Runnable(){	public void run(){ exec_Code() ;} },"Solver",1l<<27).start() ;
	}
	static void exec_Code(){
		try{
			Solver Machine = new Solver() ;
			Machine.Solve() ; Machine.Finish() ;}
		catch(Exception e){ e.printStackTrace() ; print_and_exit() ;}
		catch(Error e){ e.printStackTrace() ; print_and_exit() ; }
	}
	static void print_and_exit(){ System.out.flush() ; System.exit(-1) ;}
}
/* Implementation of the Reader class */
class Reader { 
	private InputStream mIs;
	private byte[] buf = new byte[1024];
	private int curChar,numChars;
	public Reader() { this(System.in); } 
	public Reader(InputStream is) { mIs = is;} 
	public int read() {
		if (numChars == -1) throw new InputMismatchException();    
		if (curChar >= numChars) {
			curChar = 0;
			try { numChars = mIs.read(buf);} catch (IOException e) { throw new InputMismatchException();}
			if (numChars <= 0) return -1;            
		}
		return buf[curChar++];
	} 
	public String nextLine(){
		int c = read();
		while (isSpaceChar(c)) c = read();        
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString() ;
	} 
	public String s(){
		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 long l(){
		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 int i(){
		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 boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; } 
	public boolean isEndOfLine(int c) { return c == '\n' || c == '\r' || c == -1; } 
}   
/* All the useful functions,constants,renamings are here*/
class Template{
	/* Constants Section */
	final int INT_MIN = Integer.MIN_VALUE ; final int INT_MAX = Integer.MAX_VALUE ;
	final long LONG_MIN = Long.MIN_VALUE ; final long LONG_MAX = Long.MAX_VALUE ;
	static long MOD = 1000000007 ;
	static Reader ip = new Reader() ;	
	static PrintWriter op = new PrintWriter(System.out) ;
	/* Methods for writing */
	static void p(Object o){ op.print(o) ; }
	static void pln(Object o){ op.println(o) ;}
	static void Finish(){ op.flush(); op.close(); }
	/* Implementation of operations modulo MOD */
	static long inv(long a){ return powM(a,MOD-2) ; }
	static long m(long a,long b){ return (a*b)%MOD ; }
	static long d(long a,long b){ return (a*inv(b))%MOD ; }
	static long powM(long a,long b){
		if(b<0) return powM(inv(a),-b) ;
		long ans=1 ;
		for( ; b!=0 ; a=(a*a)%MOD , b/=2) if((b&1)==1) ans = (ans*a)%MOD ;
		return ans ;
	}
	/* Renaming of some generic utility classes */
	final static class mylist extends ArrayList<Integer>{}
	final static class myset extends TreeSet<Integer>{}
	final static class mystack extends Stack<Integer>{}
	final static class mymap extends TreeMap<Integer,Integer>{}
}
/* Implementation of the pair class, useful for every other problem */
class pair implements Comparable<pair>{
	int x ; int y ;
	pair(int _x,int _y){ x=_x ; y=_y ;} 
	public int compareTo(pair p){
		return (this.x<p.x ? -1 : (this.x>p.x ? 1 : (this.y<p.y ? -1 : (this.y>p.y ? 1 : 0)))) ;
	}
}
/* Main code starts here */
class Solver extends Template{
	long aux[] = new long[10000] ;
	public void Solve() throws IOException{
		long n = ip.l() ; int k = ip.i() ;
		long dp[] = new long[k+1] ;
		long aux[] = new long[k+1] ;
		dp[0] = 1 ;
		for(int itr=1 ; itr<=k ; itr++){
			Arrays.fill(aux,0) ;
			for(int i=0 ; i<k ; i++){
				aux[i] = (aux[i]+(i*dp[i]))%MOD ;
				aux[i+1] = ((n-i)*dp[i]+aux[i+1])%MOD ;
			}
			for(int i=0 ; i<=k ; i++) dp[i] = aux[i] ;
		}
		long res=0 ;
		for(int i=0 ; i<=k ; i++) res = (res+m(powM(2,n-i),dp[i]))%MOD ;
		pln(res) ;
	}
}