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
def solve():
    mod = 10**9+7
    n, k = map(int, input().split())
    m = min(n-1,k)
    ans = 1
    dp0 = [1]*(m+1)
    dp1 = [1]*(m+1)
    for i in range(1,m+1):
        dp0[i] = dp0[i-1]*(n-i+1)*pow(i,mod-2,mod)%mod
        dp1[i] = dp1[i-1]*(n-i)*pow(i,mod-2,mod)%mod
        ans += dp0[i]*dp1[i]%mod
        ans %= mod
    return ans
print(solve())
