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)

use std::cmp::*;
use std::io::*;
const MOD: u64 = 1_000_000_007;

mod enumeration {
    pub struct Enumeration {
        fact: Vec<u64>,
        finv: Vec<u64>,
        modulo: u64,
    }
    impl Enumeration {
        pub fn new(n: usize, modulo: u64) -> Enumeration {
            let mut fact: Vec<u64> = vec![1; n];
            let mut inv: Vec<u64> = vec![1; n];
            let mut finv: Vec<u64> = vec![1; n];
            for i in 2..n {
                fact[i] = fact[i - 1] * (i as u64) % modulo;
                inv[i] = modulo - (modulo / (i as u64)) * inv[(modulo as usize % i)] % modulo;
                finv[i] = inv[i] * finv[i - 1] % modulo;
            }
            Enumeration {
                fact: fact,
                finv: finv,
                modulo: modulo,
            }
        }
        pub fn c(&self, n: usize, k: usize) -> u64 {
            if n < k {
                return 0;
            }
            self.fact[n] * self.finv[n - k] % self.modulo * self.finv[k] % self.modulo
        }
    }
}
fn main() {
    let mut s: String = String::new();
    std::io::stdin().read_to_string(&mut s).ok();
    let mut itr = s.trim().split_whitespace();
    let n: usize = itr.next().unwrap().parse().unwrap();
    let k: usize = itr.next().unwrap().parse().unwrap();

    let en = enumeration::Enumeration::new(n + n, MOD);
    // i: 0人の部屋の数
    let mut ans = 0;
    for i in 0..min(n, k + 1) {
        ans = (ans + en.c(n, i) * en.c(n - 1, (n - i) - 1) % MOD) % MOD;
    }
    println!("{}", ans);
}