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)

// -*- coding:utf-8-unix -*-

use proconio::input;

use num_traits::{pow, One};
use std::ops::{Add, Div, Mul, Sub};

const MODULUS: usize = 1000000007;

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

    // prepare a table of factorials
    let mut fac_vec: Vec<ModP> = Vec::new();
    let mut fac_inv_vec: Vec<ModP> = Vec::new();
    fac_vec.push(ModP(1));
    fac_inv_vec.push(ModP(1));
    for i in 1..(n + 1) {
        fac_vec.push(ModP(i) * fac_vec[i - 1]);
        fac_inv_vec.push(ModP(1) / 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 = ModP(0);
    for i in 0..(k + 1) {
        let thispart = fac_vec[n]
            * fac_inv_vec[i]
            * fac_inv_vec[n - i]
            * fac_vec[n - 1]
            * fac_inv_vec[n - i - 1]
            * fac_inv_vec[i];
        total = total + thispart;
    }

    println!("{}", total.0);
}

#[derive(Clone, Copy, PartialEq, Debug)]
struct ModP(usize);

impl One for ModP {
    fn one() -> Self {
        return ModP(1);
    }
}
impl Add for ModP {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        return ModP((self.0 + rhs.0) % MODULUS);
    }
}
impl Sub for ModP {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        return ModP((self.0 + MODULUS - rhs.0) % MODULUS);
    }
}
impl Mul for ModP {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        return ModP((self.0 * rhs.0) % MODULUS);
    }
}
impl Div for ModP {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        if rhs.0 == 0 {
            panic!("Tried to divide by ModP(0)!");
        }
        let rhs_inv = pow(rhs, MODULUS - 2);
        return self * rhs_inv;
    }
}