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(non_snake_case, unused_mut)]
//use petgraph::unionfind::UnionFind;
//use proconio::marker::Usize1;
use proconio::{fastout, input};
//use proconio::marker::*;
//use std::collections::*;

const MOD: i64 = 1_000_000_000 + 7;

#[fastout()]
fn main() {
    input! {
        n:usize,k:usize
    }
    // n-1 <=k のように、kが十分大きければ、全パターン。
    // すなわち n人と仕切りn-1で組み合わせなので、2n-1 choose n-1
    let mut fact = vec![1i64; n * 2];
    let mut ifact = vec![1i64; n * 2];
    for i in 1..2 * n as usize {
        fact[i] = fact[i - 1] * (i as i64) % MOD;
        ifact[i] = modInv(fact[i]);
    }
    let choose = |n, r| fact[n] * ifact[n - r] % MOD * ifact[r] % MOD;
    if n - 1 <= k {
        let ans: i64 = choose(2 * n - 1, n - 1);
        println!("{}", ans);
        return;
    }
    // k < n-1 の時は、0人の部屋の数を i とすると、0の位置がchoose(n,i)
    // i人がn-i個の部屋に分散したと考えるとその分け方は、H(n-i,i) =　choose(n-i+i-1,n-i-1)
    let mut ans = 0;
    for i in 0..=k {
        let tmp = choose(n, i) * choose(n - 1, n - i - 1) % MOD;
        //println!("i={}, choose={}", i, tmp);
        ans = (ans + tmp) % MOD;
    }
    println!("{}", ans);
}

fn modPow(x: i64, a: i64) -> i64 {
    if a == 0 {
        1
    } else {
        if a % 2 != 0 {
            modPow(x, a - 1) * x % MOD
        } else {
            let y = modPow(x, a / 2);
            y * y % MOD
        }
    }
}
fn modInv(x: i64) -> i64 {
    modPow(x, MOD - 2) % MOD
}