Sets
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Given numbers $$$n$$$ and $$$k$$$.

Let $$$[n]$$$ be the set of all numbers from $$$1$$$ to $$$n$$$.

A set $$$A$$$ is a subset of $$$B$$$ if for every $$$a\in A$$$, $$$a$$$ also belongs to $$$B$$$. The empty set ($$$\emptyset$$$) is a subset of any set.

It is necessary to find the value of the function $$$f([n],k)$$$.

$$$f([n],1)$$$ returns the number of subsets in the set $$$[n]$$$.

$$$f([n],k)$$$ where $$$k>1$$$ returns the sum $$$f(s,k-1)$$$ where $$$s$$$ is a subset of $$$[n]$$$.

Input

The first line contains two integers $$$(1\le n,k \le 10^9)$$$.

Output

It is necessary to output $$$f([n],k)$$$. Since the answer may be too large, output it modulo $$$10^9+7$$$.

Scoring

In this problem, there are conditional blocks. If your solution works correctly for certain constraints, it will receive a certain number of points. Note that the evaluation is still in the testing phase.

1. ($$$5$$$ points): $$$k=1$$$;
2. ($$$5$$$ points): $$$n\le 10$$$, $$$k\le 2$$$;
3. ($$$10$$$ points): $$$n\le 15$$$, $$$k\le 3$$$;
4. ($$$80$$$ points): without additional constraints.

Examples

Input

    1 1

Output

    2

Input

    2 2

Output

    9

Input

    3 3

Output

    64

Note

In the first example, the set with $$$1$$$ element $$$(\{1\})$$$ and $$$k=1$$$, so $$$f(\{1\},1)$$$=2 $$$(\{1\}$$$ and $$$\{\emptyset\})$$$.

In the second example, the set with $$$2$$$ elements $$$(\{1,2\})$$$ and $$$k=2$$$. $$$f(\{1,2\},2)=f(\{1,2\},1)+f(\{1\},1)+$$$ $$$+f(\{2\},1)+f(\{\emptyset\},1)=4+2+2+1=9$$$.