Problem:
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

Solution in Python (3.8.2) (judge verdict: Runtime Error)

t1,t2=map(int,input().split())
a1,a2=map(int,input().split())
b1,b2=map(int,input().split())
if a1==b1 and b2==a2:print(0)
elif t1*(a1-b1)+t2*(-b2+a2)==0:print('infinity')
else:
    if t1*(a1-b1)+t2*(-b2+a2)<0:a1,a2,b1,b2=b1,b2,a1,a2
    if t1*(a1-b1)>0:print(0)
    else:
        #(ng,ok]type
        ok,ng=10**40000,-1
        ng,ok=ok,ng
        eps=10**(-8)
        while abs(ok-ng)>1:
            mid=(ok+ng)//2
            if t1*(b1-a1)-mid>=0:ok=mid
            else:ng=mid
        print(2*(mid//(t1*(a1-b1)+t2*(-b2+a2))+1)-1-int(not mid%(t1*(a1-b1)+t2*(-b2+a2))))