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 std::io;
use std::io::Read;

const modulus :usize = 1000000007;

fn main(){
    let mut stdin = io::stdin();
    let mut lines_str = String::new();
    let _ = stdin.read_to_string(&mut lines_str);
    let lines_vec = lines_str.lines().collect::<Vec<&str>>();
    let line0_vec = lines_vec[0].split(' ').collect::<Vec<&str>>();
    let n :usize = line0_vec[0].trim().parse().unwrap(); //n >= 3
    let mut k :usize = line0_vec[1].trim().parse().unwrap(); //k >= 2

    // prepare a table of factorials
    let mut fac_vec :Vec<usize> = Vec::new();
    let mut fac_inv_vec :Vec<usize> = Vec::new();
    fac_vec.push(1);
    fac_inv_vec.push(1);
    for i in 1..(n+1) {
        fac_vec.push((i*fac_vec[i-1]) % modulus);
        fac_inv_vec.push(mod_inv(fac_vec[i]));
    }
    let fac_vec = fac_vec;
    let fac_inv_vec = fac_inv_vec;

    // normalize k
    if k >= n {
        k = n - 1;
    }
    let k = k;

    let mut total = 0;
    for i in 0..(k+1) {
        let mut thispart = (fac_vec[n] * fac_inv_vec[i]) % modulus;
        thispart = (thispart * fac_inv_vec[n-i]) % modulus;
        thispart = (thispart * fac_vec[n-1]) % modulus;
        thispart = (thispart * fac_inv_vec[n-i-1]) % modulus;
        thispart = (thispart * fac_inv_vec[i]) % modulus;
        total = (total + thispart) % modulus;
    }

    println!("{}", total);
}

// https://math.nakaken88.com/textbook/cp-modulo-operation-inverse-element/
fn mod_pow(base :usize, index :usize) -> usize {
    if index == 0 {
        return 1;
    } else if index == 1 {
        return base % modulus;
    } else {
        if index % 2 == 0 {
            let tmp = mod_pow(base, index/2);
            return (tmp * tmp) % modulus;
        } else {
            let tmp = mod_pow(base, index/2);
            return (((tmp * tmp) % modulus) * base ) % modulus;
        }
    }
}

fn mod_inv(x :usize) -> usize {
    return mod_pow(x, modulus-2);
}