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
import math
import sys

sys.setrecursionlimit(10**9)

MOD = 10**9+7

n, k = map(int, input().split())
k = min(k, n-1)

fact = [1]
for i in range(1, 10**6):
    fact.append((fact[i-1]*i)%MOD)

inv = [None]*10**6
def inv_fact(n):
    if inv[n] == None:
        inv[n] = pow(fact[n], MOD-2, MOD)
    return inv[n]

def comb(n, r):
    return (fact[n]*inv_fact(n-r)*inv_fact(r))%MOD

ans = 0
for i in range(k+1):
    ans = (ans + comb(n-1, i)*comb(n, i))%MOD
print(ans)