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 modpow(a, n, mod):
    res = 1
    while n > 0:
        if n & 1:
            res = res * a % mod
        a = a * a % mod
        n >>= 1
    return res

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

MOD = 1000000007

if n-1 > k:
    ans = 1
    com1 = 1
    com2 = 1
    for i in range(k):
        com1 = com1 * (n-1-i) * modpow(i+1, MOD-2, MOD) % MOD
        com2 = com2 * (n-i) * modpow(i+1, MOD-2, MOD) % MOD
        ans += com1 * com2
    print(ans % MOD)
else:
    ans = 1
    for i in range(n-1):
        ans = ans * (n*2-1-i) * modpow(i+1, MOD-2, MOD) % MOD
    print(ans % MOD)