Contest Duration: - (local time) (100 minutes) Back to Home
E - Roaming /

Time Limit: 2 sec / Memory Limit: 1024 MB

問題文

n 個の部屋がある建物があります。 部屋には 1 から n までの番号が付いています。

ここで、建物のある部屋 i にいる人が、別の部屋 j~ (i \neq j) に移ることを 人の移動 と呼ぶことにします。

このあと現在までに、人の移動がちょうど k 回起きたことが分かっています。

(10^9 + 7) で割った余りを求めてください。

制約

• 入力は全て整数である。
• 3 \leq n \leq 2 \times 10^5
• 2 \leq k \leq 10^9

入力

n k


入力例 1

3 2


出力例 1

10


• (0, 0, 3)
• (0, 1, 2)
• (0, 2, 1)
• (0, 3, 0)
• (1, 0, 2)
• (1, 1, 1)
• (1, 2, 0)
• (2, 0, 1)
• (2, 1, 0)
• (3, 0, 0)

10 通りです。

入力例 2

200000 1000000000


出力例 2

607923868


入力例 3

15 6


出力例 3

22583772


Score : 500 points

Problem Statement

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).

Sample Input 1

3 2


Sample Output 1

10


Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

• (0, 0, 3)
• (0, 1, 2)
• (0, 2, 1)
• (0, 3, 0)
• (1, 0, 2)
• (1, 1, 1)
• (1, 2, 0)
• (2, 0, 1)
• (2, 1, 0)
• (3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000


Sample Output 2

607923868


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

Sample Input 3

15 6


Sample Output 3

22583772