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
import sys
sys.setrecursionlimit(10000000)
input=sys.stdin.readline
mod = 10 ** 9 + 7

n,k = map(int,input().split())

fac = [1]*(n+1)
inv = [1]*(n+1)
for i in range(1,n+1):
  fac[i] = (fac[i-1]*i) % mod  
inv[n] = pow(fac[n], mod-2, mod)
for i in range(n, 0, -1):
  inv[i-1] = (inv[i]*i) % mod
    
def cmb(n, r):
     
  if r < 1:
        return 1
  return (((fac[n] * inv[r])%mod) * inv[n-r]) % mod
 


ans=0
k=min(k,n-1)
for i in range(k+1):
    ans += cmb(n,i) * cmb(n-1,i) %mod

print(ans%mod)


