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)

#![allow(unused_parens)]
#![allow(unused_imports)]
#![allow(non_upper_case_globals)]
#![allow(non_snake_case)]
#![allow(unused_mut)]
#![allow(unused_variables)]
#![allow(dead_code)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::{Chars, Usize1};

#[allow(unused_macros)]
#[cfg(debug_assertions)]
macro_rules! mydbg {
    //($arg:expr) => (dbg!($arg))
    //($arg:expr) => (println!("{:?}",$arg));
      ($($a:expr),*) => {
          eprintln!(concat!($(stringify!($a), " = {:?}, "),*), $($a),*);
      }
}
#[cfg(not(debug_assertions))]
macro_rules! mydbg {
    ($($arg:expr),*) => {};
}

macro_rules! echo {
    ($($a:expr),*) => {
          $(println!("{}",$a))*
      }
}

use std::cmp::*;
use std::collections::*;
use std::ops::{Add, Div, Mul, Sub};

#[allow(dead_code)]
static INF_I64: i64 = 92233720368547758;
#[allow(dead_code)]
static INF_I32: i32 = 21474836;
#[allow(dead_code)]
static INF_USIZE: usize = 18446744073709551;
#[allow(dead_code)]
static M_O_D: usize = 1000000007;
#[allow(dead_code)]
static PAI: f64 = 3.1415926535897932;

trait IteratorExt: Iterator {
    fn toVec(self) -> Vec<Self::Item>;
}

impl<T: Iterator> IteratorExt for T {
    fn toVec(self) -> Vec<Self::Item> {
        self.collect()
    }
}

trait CharExt {
    fn toNum(&self) -> usize;
    fn toAlphabetIndex(&self) -> usize;
    fn toNumIndex(&self) -> usize;
}
impl CharExt for char {
    fn toNum(&self) -> usize {
        return *self as usize;
    }
    fn toAlphabetIndex(&self) -> usize {
        return self.toNum() - 'a' as usize;
    }
    fn toNumIndex(&self) -> usize {
        return self.toNum() - '0' as usize;
    }
}

trait VectorExt {
    fn joinToString(&self, s: &str) -> String;
}
impl<T: ToString> VectorExt for Vec<T> {
    fn joinToString(&self, s: &str) -> String {
        return self
            .iter()
            .map(|x| x.to_string())
            .collect::<Vec<_>>()
            .join(s);
    }
}

trait StringExt {
    fn get_reverse(&self) -> String;
}
impl StringExt for String {
    fn get_reverse(&self) -> String {
        self.chars().rev().collect::<String>()
    }
}

trait UsizeExt {
    fn pow(&self, n: usize) -> usize;
}
impl UsizeExt for usize {
    fn pow(&self, n: usize) -> usize {
        return ((*self as u64).pow(n as u32)) as usize;
    }
}

#[derive(Debug, Copy, Clone)]
pub struct ModInt {
    x: i64,
    global_mod: i64,
}
impl ModInt {
    pub fn new(p: i64) -> Self {
        let gm = 1000000007;
        let a = (p % gm + gm) % gm;
        return ModInt {
            x: a,
            global_mod: gm,
        };
    }
    pub fn inv(self) -> Self {
        return self.pow(self.global_mod - 2);
    }
    pub fn pow(self, t: i64) -> Self {
        if (t == 0) {
            return ModInt::new(1);
        };
        let mut a = self.pow(t >> 1);
        a = a * a;
        if (t & 1 != 0) {
            a = a * self
        };
        return a;
    }
}
impl Add for ModInt {
    type Output = ModInt;
    fn add(self, other: ModInt) -> ModInt {
        let ret = self.x + other.x;
        return ModInt::new(ret);
    }
}
impl Sub for ModInt {
    type Output = ModInt;
    fn sub(self, other: ModInt) -> ModInt {
        let ret = self.x - other.x;
        return ModInt::new(ret);
    }
}
impl Mul for ModInt {
    type Output = ModInt;
    fn mul(self, other: ModInt) -> ModInt {
        let ret = self.x * other.x;
        return ModInt::new(ret);
    }
}
impl Div for ModInt {
    type Output = ModInt;
    fn div(self, other: ModInt) -> ModInt {
        let ret = self.x * other.inv().x;
        return ModInt::new(ret);
    }
}
impl std::string::ToString for ModInt {
    fn to_string(&self) -> String {
        return self.x.to_string();
    }
}
pub struct Combination {
    fact: Vec<ModInt>,
    ifact: Vec<ModInt>,
}
impl Combination {
    pub fn new(n: i32) -> Self {
        if n > 3000000 {
            panic!("error");
        }
        let mut fact = vec![ModInt::new(0); (n + 1) as usize];
        let mut ifact = vec![ModInt::new(0); (n + 1) as usize];
        fact[0] = ModInt::new(1);
        for i in 1..n + 1 {
            fact[i as usize] = fact[(i - 1) as usize] * ModInt::new(i as i64)
        }
        ifact[n as usize] = fact[n as usize].inv();
        for i in (1..n + 1).rev() {
            ifact[(i - 1) as usize] = ifact[i as usize] * ModInt::new(i as i64)
        }
        let a = Combination {
            fact: fact,
            ifact: ifact,
        };
        return a;
    }
    #[macro_use]
    pub fn gen(&mut self, n: i32, k: i32) -> ModInt {
        if (k < 0 || k > n) {
            return ModInt::new(0 as i64);
        };
        return self.fact[n as usize] * self.ifact[k as usize] * self.ifact[(n - k) as usize];
    }
    pub fn P(&mut self, n: i32, k: i32) -> ModInt {
        self.fact[n as usize] * self.ifact[(n - k) as usize]
    }
}

fn main() {
    input! {
       N: i32,
       K:i32
    }

    let mut ans = ModInt::new(0);
    let mut cmb = Combination::new(200005);
    for i in 0..min(N, K + 1) {
        let a = cmb.gen(N, i);
        let b = cmb.gen(N - 1, i);
        ans = ans + (a * b);
    }

    echo!(ans.to_string());
}