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.Arrays;
import java.util.Scanner;

public class e {
	static long m = (long)(1e9+7);
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		int n = in.nextInt(), k = in.nextInt();
		long[] fall = new long[k+1];
		fall[0] = 1;
		for(int i=1;i<=k;i++)
			fall[i] = (fall[i-1] * (n-i+1))%m;
		long[] m1 = new long[k+1], m2 = new long[k+1];
		for(int p=0;p<=k;p++)
			m1[p] = (fall[p] * pow(2, n-p)) % m;
		for(int i=1;i<=k;i++) {
			for(int p=0;p<k;p++)
				m2[p] = (m1[p+1] + p * m1[p]) % m;
			long[] t = m1;
			m1 = m2;
			m2 = t;
		}
		System.out.println(m1[0]);
	}
	static long pow(long x, int exp) {
		long ans = 1;
		while(exp > 0) {
			if((exp & 1) == 1)
				ans = ans * x % m;
			x = x * x % m;
			exp >>= 1;
		}
		return ans;
	}
}