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 main():
    n,k = map(int, input().split())
    MOD = 10**9+7

    # 0人部屋が0~k個の時の場合の数の和
    # Σ(i=[0,k]){comb(n,i)*pow((n-i),i)} を求めれば良い
    # しかし上式ではpowの計算量がデカすぎるので、捉え方を変えて下式まで変形
    # Σ(i=[0,k]){comb(n,i)*comb((n-1),i)} を求めれば良い
    # 注:i=0のとき、つまり0人部屋がない、つまり全部屋に1人ずつ、のケースは1通り
    # comb(n,i+1) = comb(n,i) * (n-i)/(i+1) であることを利用する
    ans = 0
    k1 = 1
    k2 = 1
    for i in range(min(k+1,n)):
        ans += k1*k2
        ans %= MOD
        k1 *= (n-i)*pow(i+1,MOD-2,MOD)
        k1 %= MOD
        k2 *= (n-1-i)*pow(i+1,MOD-2,MOD)
        k2 %= MOD
    print(int(ans))

main()
