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())
K = min(N-1, K)
fact = [1 for _ in range(200001)]
inv = [1 for _ in range(200001)]
fact_inv = [1 for _ in range(200001)]
mod = 10**9+7
for i in range(2, 200001):
    fact[i] = (fact[i-1]*i) % mod
    inv[i] = mod - (inv[mod % i] * (mod // i)) % mod
    fact_inv[i] = (fact_inv[i-1] * inv[i]) % mod

dp = [0] * N
for i in range(N):
    f1 = (fact[N] * fact_inv[N-i] * fact_inv[i]) % mod  
    f2 = (fact[N-1] * fact_inv[N-i-1] * fact_inv[i]) % mod 
    f = (f1*f2)%mod
    if i == 0:
        dp[i] = f
    else:
        dp[i] = (dp[i-1] + f) % mod
print(dp[K])