Problem Statement

You are given integers N and A.
You will perform the following operations:

• Generate N real numbers uniformly at random between 0 and 1, inclusive. All generations are independent, and the random numbers are uniformly distributed.
• Call the generated $N real numbers x_1, x_2, \cdots, x_N$ in ascending order. That is$, 0 \leq x_1 \leq x_2 \leq \cdots \leq x_N \leq 1$.
• Your score is given by the following formula:

$\displaystyle \prod_{i=1}^{N} \left(1+\sum_{j=i+1}^N x_j^A \right)$
Calculate the expected value, modulo 10^9+7, of the score.

Definition of expected value modulo 10^9+7
It can be proved that the sought expected value is always rational. Furthermore, under the constraints of this problem, it can be proved that if the expected value is expressed as an irreducible fraction $\frac{P}{Q}$, then $Q \neq 0 \pmod{10^9+7}. Therefore, there exists a unique integer R$ such that $R \times Q \equiv P \pmod{10^9+7}, 0 \leq R < 10^9+7.$ Report this R.

Input

The input is given from Standard Input in the following format:
N A

Output

Print the answer.

Constraints

• $1 \leq N \leq 10^4$
• $1 \leq A \leq 5 \times 10^4$
• All input values are integers.

Sample Input 1

2 1

Sample Output 1

666666673

The expected value of the score is 5/3.

Sample Input 2

1 1

Sample Output 2

1

Sample Input 3

2 2

Sample Output 3

500000005

Sample Input 4

3 2

Sample Output 4

142857147

Sample Input 5

5 3

Sample Output 5

758371066

Sample Input 6

10000 12345

Sample Output 6

32201773

见题面 Input 部分

见题面 Output 部分