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::vec::Vec;
use std::cmp::min;


fn read<T: std::str::FromStr>() -> T {
    let mut s = String::new();
    std::io::stdin().read_line(&mut s).ok();
    s.trim().parse().ok().unwrap()
}

fn read_vec<T: std::str::FromStr>() -> Vec<T> {
    read::<String>().split_whitespace().map(|e| e.parse().ok().unwrap()).collect()
}

fn read_touple<T: std::str::FromStr + Copy>() -> (T, T) {
  let v: Vec<T> = read_vec();
  assert_eq!(v.len(), 2);
  (v[0], v[1])
}

const MOD: usize = 1_000_000_000 + 7;

fn main() {
    let (n, k) = read_touple::<usize>();

    let mdc = ModConb::new(2 * n);

    let ans = (0..min(n-1, k)+1)
                .fold(
                    Mod::new_zero(), 
                    |acc, m| mdc.get(n, m) * mdc.get(n-1, n-m-1) + acc);
    println!("{}", ans.unwrap());
}


#[derive(Debug, Clone, Copy, Eq, PartialEq, Ord, PartialOrd)]
struct Mod {
  val: usize,
}

// 和を定義
impl std::ops::Add for Mod {
  type Output = Mod;
  // O(1)
  fn add(self, other: Mod) -> Mod {
    Mod {
      val: (self.val + other.val) % MOD,
    }
  }
}

// 差を定義
impl std::ops::Sub for Mod {
  type Output = Mod;

  // O(1)
  fn sub(self, other: Mod) -> Mod {
    Mod {
      val: (self.val + MOD - other.val) % MOD,
    }
  }
}

// 積を定義
impl std::ops::Mul for Mod {
  type Output = Mod;

  // O(1)
  fn mul(self, other: Mod) -> Mod {
    Mod {
      val: (self.val * other.val) % MOD,
    }
  }
}

// 加法単位元
impl std::ops::Neg for Mod {
  type Output = Mod;

  // O(1)
  fn neg(self) -> Mod {
    Mod {
      val: MOD - self.val,
    }
  }
}

// 逆元を定義
// フェルマーの小定理により実装
impl std::ops::Div for Mod {
  type Output = Mod;

  //O(logN)
  fn div(self, other: Mod) -> Mod {
    self * other.inv()
  }
}

impl Mod {
  // コンストラクター
  fn new(n: usize) -> Mod {
    Mod { val: n % MOD }
  }

  // 加法単位元
  fn new_zero() -> Mod {
    Mod { val: 0 }
  }

  // 乗法単位元
  fn new_one() -> Mod {
    Mod { val: 1 }
  }

  // 加法逆元
  // 上記にて定義

  // 乗法逆元
  fn inv(self) -> Mod {
    if self.val == 0 {
      panic!("zero divide");
    }
    self.pow(MOD - 2)
  }

  // 累乗を定義
  // O(logN)
  fn pow(self, n: usize) -> Mod {
    let mut res = 1;
    let mut a = self.unwrap();
    let mut n = n;

    while n > 0 {
      if n % 2 == 0 {
        a = a * a;
        n /= 2;
      } else {
        res = res * a;
        a = a * a;
        n /= 2;
      }
      res %= MOD;
      a %= MOD;
    }
    Mod::new(res)
  }

  // 最大公約数
  // O(logN)
  fn gcd(self, other: Mod) -> usize {
    let mut x = self.val;
    let mut y = other.val;
    while y != 0 {
      let t = y;
      y = x % y;
      x = t;
    }
    x
  }

  // 階乗
  // O(N)
  fn fact(self) -> Mod {
    let mut res = 1;
    for i in 1..self.val + 1 {
      res *= i;
      res %= MOD;
    }

    Mod::new(res)
  }

  // 順列
  fn perm(self, other: Mod) -> Mod {
    let mut res = Mod::new_one();
    for x in (self.val - other.val + 1)..self.val + 1 {
      res = res * Mod::new(x);
    }

    res
  }

  // 組み合わせ O(N)
  fn conb(self, other: Mod) -> Mod {
    if self < other {
      return Mod::new_zero();
    }
    self.fact() / (other.fact() * (self - other).fact())
  }

  fn unwrap(self) -> usize {
    self.val % MOD
  }
}

#[derive(Debug, Clone, Eq, PartialEq, Ord, PartialOrd)]
struct ModConb {
  fact: Vec<Mod>,
  inv_fact: Vec<Mod>,
  n: usize,
}

impl ModConb {
  // O(N)
  fn new(n: usize) -> ModConb {
    let mut fact = vec![Mod::new_one(); n + 1];
    let mut inv_fact = vec![Mod::new_one(); n + 1];
    for i in 1..(n + 1) {
      fact[i] = fact[i - 1] * Mod::new(i);
      inv_fact[i] = inv_fact[i - 1] / Mod::new(i);
    }

    ModConb {
      fact: fact,
      inv_fact: inv_fact,
      n: n + 1,
    }
  }
  // O(1)
  fn get(&self, n: usize, r: usize) -> Mod {
    if r <= n {
      self.fact[n] * self.inv_fact[r] * self.inv_fact[n - r]
    } else {
      Mod::new_zero()
    }
  }
}