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
MOD = 1000000007  # type: int
 
def solve(n: int, k: int):
    fact = [1] * (n+1)
    inv_fact = [1] * (n+1)
    for i in range(1, n+1):
        fact[i] = i*fact[i-1] % MOD
 
    inv_fact[-1] = pow(fact[-1], MOD-2, MOD)
    for i in range(n-1, 0, -1):
        inv_fact[i] = inv_fact[i+1] * (i+1) % MOD
 
    def comb(n, r, MOD=MOD):
        return fact[n] * inv_fact[n-r] * inv_fact[r] % MOD
    
    ans = 0
    for i in range(min(k, n-1)+1):
        ans += comb(n, i) * comb(n-1, i) % MOD
        ans %= MOD
 
    return ans

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

print(solve(n, k))