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 (1.42.0) (judge verdict: Accepted)

use proconio::input;
use std::cmp;

fn main() {
    input! {
        n: usize,
        k: usize,
    }

    let max = 510000;
    let m = 1000000007;

    let mut fac = vec![0; max];
    let mut finv = vec![0; max];
    let mut inv = vec![0; max];

    let mut ans = 0;
    com_init(&mut fac, &mut finv, &mut inv, max, m);
    for i in 0..cmp::min(n, k+1) {
        ans += com(n, i, &fac, &finv, m) * com(n - 1, n - i - 1, &fac, &finv, m) % m;
        ans %= m;
    }
    println!("{}", ans);
}

fn com_init(
    fac: &mut Vec<isize>,
    finv: &mut Vec<isize>,
    inv: &mut Vec<isize>,
    max: usize,
    m: isize,
) {
    fac[0] = 1;
    fac[1] = 1;
    finv[0] = 1;
    finv[1] = 1;
    inv[0] = 0;
    inv[1] = 1;

    let mut i = 2;
    while i < max {
        fac[i] = fac[i - 1] * i as isize % m;
        inv[i] = m as isize - inv[m as usize % i] * (m / i as isize) % m;
        finv[i] = finv[i - 1] * inv[i] % m;
        i += 1;
    }
}

fn com(n: usize, k: usize, fac: &Vec<isize>, finv: &Vec<isize>, m: isize) -> isize {
    if n < k {
        return 0;
    }
    fac[n] * (finv[k] * finv[n - k] % m) % m
}