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::min;

const MOD: i64 = 1000000007;


fn main() {
    let (n, k) = read_tuple();

    let c = Comb::new(2 * n + 1, MOD);

    let mut ans = 0;
    for m in 0..(min(n, k + 1)) {
        ans += (c.nck(n, m) * c.nck(n - 1, m)) % MOD;
        ans %= MOD;
    }
    
    println!("{:?}", ans);
}


/// for nCk
pub struct Comb {
    max: usize,
    m: i64,
    fac: Vec<i64>,
    finv: Vec<i64>,
}

impl Comb {
    /// initialize table 
    /// max: maximum that n as nCk takes
    /// m: MOD, a prime number
    /// O(n)
    pub fn new(max: usize, m: i64) -> Comb {
        let n = max;
        let mut fac = Vec::with_capacity(n);
        fac.push(1);
        fac.push(1);
        let mut finv = Vec::with_capacity(n);
        finv.push(1);
        finv.push(1);
        let mut inv = Vec::with_capacity(n);
        inv.push(1);
        inv.push(1);

        for i in 2..n {
            let i = i as i64;
            let tmp = fac.last().unwrap() * i % m;
            fac.push(tmp);
            let tmp = m - inv[(m % i) as usize] * (m / i) % m;
            inv.push(tmp);
            let tmp = finv.last().unwrap() * inv.last().unwrap() % m;
            finv.push(tmp);
        }

        Comb {
            max: max,
            m: m,
            fac: fac,
            finv: finv
        }
    }

    /// nCk
    pub fn nck(&self, n: usize, k: usize) -> i64 {
        // since n, k are usize, do not need to check `n < 0 || k < 0`
        if n < k || n > self.max {
            panic!("Invalid query (n, k) = ({}, {})", n, k);
        } else {
            self.fac[n] * (self.finv[k] * self.finv[n - k] % self.m) % self.m
        }
    }
}


fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().split_whitespace()
        .map(|e| e.parse().ok().unwrap()).collect()
}
fn read_tuple<T: std::str::FromStr + Copy>() -> (T, T) {
    let temp = read_vec();
    (temp[0], temp[1])
}