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
N ,K = map(int, input().split())
MOD = 10**9 + 7
ans = 0

S = [0]*(2*10**5+1)
S[1] = 1
for i in range(2, 2*10**5+1):
    S[i] = S[MOD%i]*(MOD-int(MOD/i))%MOD

if N-1 <= K:
    ans = 1
    num = 2*N - 1
    for i in range(N-1):
        ans *= (num-i)*S[i+1]
        ans %= MOD
    print(ans%MOD)
else:
    S1 = [1]*N
    S2 = [1]*N
    for i in range(1, N):
        S1[i] = (S1[i-1]*(N+1-i)*S[i])%MOD
        S2[i] = (S2[i-1]*(N-i)*S[i])%MOD
    ans = 0
    for i in range(K+1):
        ans += S1[i]*S2[N-1-i]
        ans %= MOD
    print(ans)


# nCm * n-mHm
# nCm * n-1Cn-m-1