Problem Description

The hospitable Little Monkey invites friends from the forest to dinner. His friends are numbered from $1$ to $N$. Each friend brings him some gifts: Big Bananas. The first friend brings him $1$ Big Banana, and each subsequent friend brings the total number of gifts from all previous friends plus his own number raised to the power of $K$. For example, if $K=2$, the number of gifts from the first few friends would be:

$1, 5, 15, 37, 83, \ldots$

If $K=3$, the number of gifts from the first few friends would be:

$1, 9, 37, 111, \ldots$

Now, Little Monkey is curious about how many gifts he will receive from the $N$-th friend and asks for your help.

Given $N$ and $K$, output the number of gifts the $N$-th friend will bring, modulo $10^9+7$.

Input Format

The first line contains two integers $N$ and $K$.

Output Format

Output a single integer, which is the number of gifts the $N$-th friend will bring, modulo $10^9+7$.

Sample Input and Output

Sample Input #1

4 2

Sample Output #1

37

Sample Input #2

2333333 2

Sample Output #2

514898185

Sample Input #3

1234567890000 3

Sample Output #3

891659731

Sample Input #4

66666666 10

Sample Output #4

32306309

Notes

• $20\%$ of the test cases: $N \le 10^6$;
• Another $10\%$ of the test cases: $K=1$;
• Another $20\%$ of the test cases: $K=2$;
• Another $20\%$ of the test cases: $K=3$;
• $100\%$ of the test cases: $N \le 10^{18}$, $K \le 10$.

见题面 Input 部分

见题面 Output 部分