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)

#![allow(unused_imports)]
#![allow(non_snake_case, unused)]

use std::cmp::*;
use std::collections::*;
use std::ops::*;

macro_rules! eprint {
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = write!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! eprintln {
	() => { eprintln!(""); };
	($($t:tt)*) => {{
		use ::std::io::Write;
		let _ = writeln!(::std::io::stderr(), $($t)*);
	}};
}
macro_rules! dbg {
	($v:expr) => {{
		let val = $v;
		eprintln!("[{}:{}] {} = {:?}", file!(), line!(), stringify!($v), val);
		val
	}}
}

macro_rules! mat {
	($($e:expr),*) => { Vec::from(vec![$($e),*]) };
	($($e:expr,)*) => { Vec::from(vec![$($e),*]) };
	($e:expr; $d:expr) => { Vec::from(vec![$e; $d]) };
	($e:expr; $d:expr $(; $ds:expr)+) => { Vec::from(vec![mat![$e $(; $ds)*]; $d]) };
}

macro_rules! ok {
	($a:ident$([$i:expr])*.$f:ident()$(@$t:ident)*) => {
		$a$([$i])*.$f($($t),*)
	};
	($a:ident$([$i:expr])*.$f:ident($e:expr$(,$es:expr)*)$(@$t:ident)*) => { {
		let t = $e;
		ok!($a$([$i])*.$f($($es),*)$(@$t)*@t)
	} };
}

pub fn readln() -> String {
	let mut line = String::new();
	::std::io::stdin().read_line(&mut line).unwrap_or_else(|e| panic!("{}", e));
	line
}

macro_rules! read {
	($($t:tt),*; $n:expr) => {{
		let stdin = ::std::io::stdin();
		let ret = ::std::io::BufRead::lines(stdin.lock()).take($n).map(|line| {
			let line = line.unwrap();
			let mut it = line.split_whitespace();
			_read!(it; $($t),*)
		}).collect::<Vec<_>>();
		ret
	}};
	($($t:tt),*) => {{
		let line = readln();
		let mut it = line.split_whitespace();
		_read!(it; $($t),*)
	}};
}

macro_rules! _read {
	($it:ident; [char]) => {
		_read!($it; String).chars().collect::<Vec<_>>()
	};
	($it:ident; [u8]) => {
		Vec::from(_read!($it; String).into_bytes())
	};
	($it:ident; usize1) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1
	};
	($it:ident; [usize1]) => {
		$it.map(|s| s.parse::<usize>().unwrap_or_else(|e| panic!("{}", e)) - 1).collect::<Vec<_>>()
	};
	($it:ident; [$t:ty]) => {
		$it.map(|s| s.parse::<$t>().unwrap_or_else(|e| panic!("{}", e))).collect::<Vec<_>>()
	};
	($it:ident; $t:ty) => {
		$it.next().unwrap_or_else(|| panic!("input mismatch")).parse::<$t>().unwrap_or_else(|e| panic!("{}", e))
	};
	($it:ident; $($t:tt),+) => {
		($(_read!($it; $t)),*)
	};
}

pub fn main() {
	let _ = ::std::thread::Builder::new().name("run".to_string()).stack_size(32 * 1024 * 1024).spawn(run).unwrap().join();
}

const MOD: usize = 1_000_000_007;
const INF: i64 = std::i64::MAX/2;

pub trait SetMinMax {
	fn setmin(&mut self, v: Self) -> bool;
	fn setmax(&mut self, v: Self) -> bool;
}
impl<T> SetMinMax for T where T: PartialOrd {
	fn setmin(&mut self, v: T) -> bool {
		*self > v && { *self = v; true }
	}
	fn setmax(&mut self, v: T) -> bool {
		*self < v && { *self = v; true }
	}
}

use std::ops::{Add, AddAssign, Div, DivAssign, Mul, MulAssign, Sub, SubAssign};

type Num = usize;

#[derive(Clone, Copy, Debug)]
pub struct ModInt<T: Copy + Clone>(pub T);

impl Add<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self + rhs.0
    }
}

impl Add<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn add(self, rhs: Num) -> ModInt<Num> {
        let mut t = rhs + self.0;
        if t >= MOD {
            t = t - MOD;
        }
        ModInt(t)
    }
}

impl Sub<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: Num) -> ModInt<Num> {
        let rhs = if rhs >= MOD { rhs % MOD } else { rhs };
        let value = if self.0 < rhs { self.0 + MOD } else { self.0 };
        ModInt(value - rhs)
    }
}

impl Sub<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn sub(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self - rhs.0
    }
}

impl AddAssign<Num> for ModInt<Num> {
    fn add_assign(&mut self, other: Num) {
        *self = *self + other;
    }
}
impl AddAssign<ModInt<Num>> for ModInt<Num> {
    fn add_assign(&mut self, other: ModInt<Num>) {
        *self = *self + other;
    }
}

impl SubAssign<Num> for ModInt<Num> {
    fn sub_assign(&mut self, other: Num) {
        *self = *self - other;
    }
}

impl SubAssign<ModInt<Num>> for ModInt<Num> {
    fn sub_assign(&mut self, other: ModInt<Num>) {
        *self = *self - other;
    }
}

impl Div<Num> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, rhs: Num) -> ModInt<Num> {
        self * ModInt(rhs).pow(MOD - 2)
    }
}

impl Div<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;
    fn div(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self / rhs.0
    }
}

impl DivAssign<Num> for ModInt<Num> {
    fn div_assign(&mut self, rhs: Num) {
        *self = *self / rhs
    }
}
impl DivAssign<ModInt<Num>> for ModInt<Num> {
    fn div_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self / rhs
    }
}

impl Mul<ModInt<Num>> for ModInt<Num> {
    type Output = ModInt<Num>;

    fn mul(self, rhs: ModInt<Num>) -> ModInt<Num> {
        self * rhs.0
    }
}
impl Mul<Num> for ModInt<Num> {
    type Output = ModInt<Num>;

    fn mul(self, rhs: Num) -> ModInt<Num> {
        let t = (self.0 * rhs) % MOD;
        ModInt(t)
    }
}

impl MulAssign<Num> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: Num) {
        *self = *self * rhs;
    }
}

impl MulAssign<ModInt<Num>> for ModInt<Num> {
    fn mul_assign(&mut self, rhs: ModInt<Num>) {
        *self = *self * rhs;
    }
}

impl ModInt<Num> {
    pub fn pow(self, e: usize) -> ModInt<Num> {
        let mut result = ModInt(1);
        let mut cur = self;
        let mut e = e;
        while e > 0 {
            if e & 1 == 1 {
                result *= cur;
            }
            e >>= 1;
            cur *= cur;
        }
        result
    }
}

pub struct Comb {
    fact: Vec<ModInt<Num>>,
    factinv: Vec<ModInt<Num>>,
}

impl Comb {
    /// Create a object that provides effiecint computation of combinations
    /// for input smaller than `n`.
    ///
    /// This requires `O(n)` time.
    pub fn new(n: usize) -> Comb {
        let mut fact: Vec<ModInt<Num>> = vec![ModInt(0); n + 1];
        let mut factinv: Vec<ModInt<Num>> = vec![ModInt(0); n + 1];
        fact[0] = ModInt(1);
        for i in 0..n {
            fact[i + 1] = fact[i] * (i + 1);
        }
        factinv[n] = fact[n].pow(MOD-2);
        for i in (0..n).rev() {
            factinv[i] = factinv[i + 1] * (i + 1);
        }
        Comb {
            fact: fact,
            factinv: factinv,
        }
    }

    /// `n! = 1 * 2 * ... * n`
    ///
    /// `O(1)` if n is smaller than input in `new` method.
    pub fn fact(&self, n: usize) -> ModInt<Num> {
        if let Some(x) = self.fact.get(n as usize) {
            *x
        } else if n >= MOD {
            ModInt(0)
        } else {
            // Note that this is slow if `n` is large.
            // Precalculation is a possible solution but doesn't work for any module number.
            let mut res = ModInt(1);
            for a in 1..(n + 1) {
                res *= a;
            }
            res
        }
    }

    /// returns `y` such that `n! * y == 1`.
    ///
    /// `O(1)` if n is smaller than input in `new` method.
    pub fn factinv(&self, n: usize) -> ModInt<Num> {
        if let Some(x) = self.factinv.get(n) {
            *x
        } else {
            self.fact(n).pow(MOD-2)
        }
    }

    /// `nPr = n! / (n - r)!`
    ///
    /// `O(1)` if n and r are smaller than input in `new` method.
    pub fn perm(&self, n: usize, r: usize) -> ModInt<Num> {
        if n >= r {
            self.fact(n) * self.factinv(n - r)
        } else {
            ModInt(0)
        }
    }

    /// `nCr = n! / (n - r)! / r!`.
    ///
    /// `O(1)` if n and r are smaller than input in `new` method.
    pub fn comb(&self, n: usize, r: usize) -> ModInt<Num> {
        let m = MOD;
        if n >= m {
            self.comb(n % m, r % m) * self.comb(n / m, r / m) // Lucas' theorem
        } else if n >= r {
            self.fact(n) * self.factinv(n - r) * self.factinv(r)
        } else {
            ModInt(0)
        }
    }
}

fn solve() {
	let (n,k) = read!(usize,usize);
	let mut s = min(n-1,k);
	let mut ans = ModInt(0);
	let mut p = s;
	let mut c = Comb::new(n);
	let mut d = Comb::new(n-1);
	loop {
		ans += c.comb(n,p)*d.comb(n-1,n-p-1);
		if p<1 {break;}
		p -= 1;
	}
	println!("{}", ans.0);
}
fn run() {
    solve();
}