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::io;
use std::cmp;
use std::collections::BinaryHeap;
use std::collections::HashMap;
use std::collections::HashSet;
use std::f64::consts::PI;

fn read_line() -> String {
    let mut buf = String::new();
    io::stdin().read_line(&mut buf).ok();
    buf
}

const MOD: i64 = 1_000_000_007;

fn extgcd(a: i64, b: i64, x: &mut i64, y: &mut i64) -> i64 {
    let mut d = a;
    if b != 0 {
        d = extgcd(b, a % b, y, x);
        *y -= (a / b) * (*x);
    } else {
        *x = 1; *y = 0;
    }
    d
}

fn mod_inverse(a: i64, m: i64) -> i64 {
    let mut x = 0;
    let mut y = 0;
    extgcd(a, m, &mut x, &mut y);
    (m + x % m) % m
}

fn mod_fact(n: i64, p: i64, e: &mut i64, fact: &Vec<i64>) -> i64 {
    *e = 0;
    if n == 0 {
        return 1;
    }

    let res = mod_fact(n/p, p, e, fact);
    *e += n/p;
    if (n/p %2 != 0) {
        return res * (p - fact[(n%p) as usize]) % p;
    }
    res * fact[(n%p) as usize] % p
}

fn mod_comb(n: i64, k: i64, memo: &Vec<i64>) -> i64 {
    if n < 0 || k < 0 || n < k {
        return 0;
    }
    let mut e1 = 0;
    let mut e2 = 0;
    let mut e3 = 0;
    let a1 = memo[n as usize];
    let a2 = memo[k as usize];
    let a3 = memo[(n-k) as usize];
    if e1 > e2 + e3 {
        return 0;
    }
    a1 * mod_inverse(a2 * a3 % MOD, MOD) % MOD
}


fn main() {
    let line: Vec<usize> = read_line().split_whitespace().map(|s| s.parse().unwrap()).collect();
    let n = line[0];
    let k = line[1];
    let mut memo = vec![0i64; 400_010];
    memo[0] = 1;
    memo[1] = 1;
    for i in 2..memo.len() {
        memo[i] = (memo[i-1] * (i as i64)) % MOD;
    }

    let mut ans = 0;
    if k >= n-1 {
        ans = mod_comb((2 * n -1) as i64, (n-1) as i64, &memo);
    } else {
        for i in 0..k+1 {
            ans += mod_comb(n as i64, i as i64, &memo) * mod_comb((n - 1) as i64, i as i64, &memo) % MOD;
            ans %= MOD;
        }
    }
    println!("{}", ans);
}