Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

(0, 0, 3)

(0, 1, 2)

(0, 2, 1)

(0, 3, 0)

(1, 0, 2)

(1, 1, 1)

(1, 2, 0)

(2, 0, 1)

(2, 1, 0)

(3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

Solution in Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x);
parseMap(x::Array{SubString{String},1}) = map(parseInt, x);

N_MAX = 2 * 10^5;
fac = Array{Int}(N_MAX+1);
inv = Array{Int}(N_MAX+1);
MOD = 10^9 + 7;
#初期化
function COMINIT();fac[1] = 1;for i in 1:N_MAX-1;fac[i+1] = fac[i] * (i+1) % MOD;end;for i in 1:N_MAX;inv[i] = powermod(fac[i], MOD-2, MOD);end;end;
#nCk
function Comb(n, k);if n <= 0 || k < 0;return 0;end;if k > n;return 0;end;if k == 0 || n == k;return 1;end;return ((fac[n] * inv[k]) % MOD * inv[n-k])%MOD;end;
function H(n, m);return Comb(n + m, m);end;
function main();COMINIT();n,k = parseInt.(split(readline()));m = min(k, n-1);ans = 0;for i in 0:m;ans += (Comb(n,i) * H(n-1-i,i)) % MOD;ans %= MOD;end;println(ans);end;
main();