Roaming

There is a building with n rooms, numbered 1 to n.

We can move from any room to any other room in the building.

Let us call the following event a move: a person in some room i goes to another room j~ (i \neq j).

Initially, there was one person in each room in the building.

After that, we know that there were exactly k moves happened up to now.

We are interested in the number of people in each of the n rooms now. How many combinations of numbers of people in the n rooms are possible?

Find the count modulo (10^9 + 7).

Constraints

• All values in input are integers.
• 3 \leq n \leq 2 \times 10^5
• 2 \leq k \leq 10^9

Input

Input is given from Standard Input in the following format:

n k

Output

Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).

Examples

Input

3 2

Output

10

Input

200000 1000000000

Output

607923868

Input

15 6

Output

22583772

inputFormat

input are integers.

• 3 \leq n \leq 2 \times 10^5
• 2 \leq k \leq 10^9

Input

Input is given from Standard Input in the following format:

n k

outputFormat

Output

Print the number of possible combinations of numbers of people in the n rooms now, modulo (10^9 + 7).

Examples

Input

3 2

Output

10

Input

200000 1000000000

Output

607923868

Input

15 6

Output

22583772

样例

3 2

10