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(clippy::needless_range_loop)]
#![allow(unused_macros)]
#![allow(dead_code)]
#![allow(unused_imports)]

use itertools::Itertools;
use proconio::input;
use proconio::marker::*;

pub const MOD: usize = 1000000007;
pub fn mint(number: usize) -> ModInt {
    ModInt(number % MOD)
}
#[derive(Copy, Clone, Eq, PartialEq, std :: fmt :: Debug)]
pub struct ModInt(pub usize);
impl std::ops::Add for ModInt {
    type Output = Self;
    fn add(self, rhs: Self) -> Self {
        ModInt((self.0 + rhs.0) % MOD)
    }
}
#[allow(clippy::suspicious_op_assign_impl)]
impl std::ops::AddAssign for ModInt {
    fn add_assign(&mut self, rhs: Self) {
        self.0 += rhs.0;
        self.0 %= MOD;
    }
}
impl std::ops::Sub for ModInt {
    type Output = Self;
    fn sub(self, rhs: Self) -> Self {
        ModInt((self.0 + MOD - rhs.0) % MOD)
    }
}
#[allow(clippy::suspicious_op_assign_impl)]
impl std::ops::SubAssign for ModInt {
    fn sub_assign(&mut self, rhs: Self) {
        self.0 += MOD - rhs.0;
        self.0 %= MOD;
    }
}
impl std::ops::Mul for ModInt {
    type Output = Self;
    fn mul(self, rhs: Self) -> Self {
        ModInt((self.0 * rhs.0) % MOD)
    }
}
#[allow(clippy::suspicious_op_assign_impl)]
impl std::ops::MulAssign for ModInt {
    fn mul_assign(&mut self, rhs: Self) {
        self.0 *= rhs.0;
        self.0 %= MOD;
    }
}
impl std::ops::Div for ModInt {
    type Output = Self;
    fn div(self, rhs: Self) -> Self {
        ModInt((self.0 * rhs.pow(MOD - 2).0) % MOD)
    }
}
#[allow(clippy::suspicious_op_assign_impl)]
impl std::ops::DivAssign for ModInt {
    fn div_assign(&mut self, rhs: Self) {
        self.0 *= rhs.pow(MOD - 2).0;
        self.0 %= MOD;
    }
}
impl std::fmt::Display for ModInt {
    fn fmt(&self, f: &mut std::fmt::Formatter<'_>) -> std::fmt::Result {
        f.write_str(&self.0.to_string())
    }
}
impl ModInt {
    pub fn pow(&self, power: usize) -> ModInt {
        let mut acc_base = *self;
        let mut acc_pow = power;
        let mut res = ModInt(1);
        while acc_pow > 0 {
            if acc_pow & 1 == 1 {
                res *= acc_base;
            }
            acc_base *= acc_base;
            acc_pow >>= 1;
        }
        res
    }
}
pub struct ModIntFact {
    memo: Vec<ModInt>,
    memo_inv: Vec<ModInt>,
    size: usize,
}
impl ModIntFact {
    pub fn new() -> Self {
        Self {
            memo: vec![ModInt(1)],
            memo_inv: vec![ModInt(1)],
            size: 0,
        }
    }
    pub fn extend(&mut self, size: usize) {
        if self.size >= size {
            return;
        }
        self.memo.resize(size + 1, ModInt(0));
        self.memo_inv.resize(size + 1, ModInt(0));
        for n in (self.size + 1)..=size {
            self.memo[n] = self.memo[n - 1] * ModInt(n);
            self.memo_inv[n] = self.memo[n].pow(MOD - 2);
        }
        self.size = size;
    }
    pub fn fact(&mut self, n: usize) -> ModInt {
        self.extend(n);
        self.memo[n]
    }
    pub fn fact_inv(&mut self, n: usize) -> ModInt {
        self.extend(n);
        self.memo_inv[n]
    }
    pub fn ncr(&mut self, n: usize, r: usize) -> ModInt {
        self.fact(n) * self.fact_inv(r) * self.fact_inv(n - r)
    }
    pub fn npr(&mut self, n: usize, r: usize) -> ModInt {
        self.fact(n) * self.fact_inv(n - r)
    }
    pub fn nhr(&mut self, n: usize, r: usize) -> ModInt {
        self.fact(n + r - 1) * self.fact_inv(r) * self.fact_inv(n - 1)
    }
}
impl std::iter::Sum for ModInt {
    fn sum<I: Iterator<Item = Self>>(iter: I) -> Self {
        iter.fold(ModInt(0), |x, y| x + y)
    }
}

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

    let mut fact = ModIntFact::new();
    fact.extend(n);
    let ans: ModInt = (0..=std::cmp::min(k, n - 1))
        .map(|x| fact.ncr(n, x) * fact.nhr(n - x, x))
        .sum();
    println!("{}", ans);
}