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 Rust (1.15.1) (judge verdict: Accepted)

fn main() {
    let (n,k) = {
        let s =rv::<u64>();
        (s[0],s[1])
    };
    let mut c=1;
    let mut h=1;
    let mut t=1;
    for i in 1..std::cmp::min(n,k+1) {
        let j =inv(i);
        c=c*(n+1-i)%MOD*j%MOD;
        h=h*(n-i)%MOD*j%MOD;
        t=(t+c*h)%MOD;
    }
    println!("{}",t);
}
const MOD: u64=1000000007;
fn inv(mut a: u64) -> u64 {
    let mut n=MOD-2;
    let mut b=1;
    while n>0 {
        if n&1==1 {
            b=b*a%MOD;
        }
        a=a*a%MOD;
        n>>=1;
    }
    b
}
fn rl() -> String {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).unwrap();
    s
}
fn rv<T>() -> Vec<T>
  where T: std::str::FromStr, T::Err: std::fmt::Debug, {
    rl().split_whitespace().map(|x|x.parse::<T>().unwrap()).collect()
}