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)

// This code is generated by [cargo-atcoder](https://github.com/tanakh/cargo-atcoder)
// Original source code:
/*
use proconio::input;
use modint::{ModInt, ModIntUtil};

// もし k >= n - 1 ならどの組み合わせも作れる
// 空き部屋はk個まで作れる

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

    let mut solver = Solve::new();

    let mut ans = ModInt::from(0);
    let min = std::cmp::min(k, n - 1);
    for r in 0..=min {
        ans += solver.count(n, k, r);
    }

    println!("{}", ans.0);
}

struct Solve {
    modint_util: ModIntUtil,
}

// 空き部屋r個
impl Solve {
    fn new() -> Solve {
        Solve { modint_util: ModIntUtil::new() }
    }

    fn count(&mut self, n: usize, k: usize, r: usize) -> ModInt {
        if r >= n {
            return ModInt::from(0);
        }
        let util = &mut self.modint_util;
        util.binom_coef(n, r) * util.binom_coef(n - 1, n - r - 1)
    }
}

mod modint {
    use std::ops::{Add, AddAssign, Mul, MulAssign, Neg, Sub, SubAssign};

    pub const MODULO: usize = 1_000_000_007;
    // pub const MODULO: usize = 11;

    fn positive_rem(a: isize, b: usize) -> usize {
        let b = b as isize;
        let mut value = a % b;
        if value < 0 {
            value += b;
        }
        // TODO: TryFrom
        value as usize
    }

    /// Return (x, y) s.t. ax + by = d where d = gcd(a, b)
    #[allow(unused)]
    pub fn ext_gcd(a: usize, b: usize) -> (isize, isize) {
        if b == 0 {
            return (1, 0);
        }

        let q = (a / b) as isize;
        let r = a % b;
        let (x1, y1) = ext_gcd(b, r);
        (y1, x1 - q * y1)
    }

    #[derive(Debug, Copy, Clone)]
    pub struct ModInt(pub usize);

    impl From<usize> for ModInt {
        fn from(n: usize) -> ModInt {
            ModInt(n % MODULO)
        }
    }

    impl From<isize> for ModInt {
        fn from(n: isize) -> ModInt {
            // TODO: use TryFrom
            ModInt(positive_rem(n, MODULO as usize))
        }
    }

    impl From<i32> for ModInt {
        fn from(n: i32) -> ModInt {
            // TODO: use TryFrom
            ModInt(positive_rem(n as isize, MODULO as usize))
        }
    }

    impl ModInt {
        #[allow(unused)]
        pub fn pow(self, p: usize) -> ModInt {
            if self == ModInt::from(0) {
                return ModInt::from(0);
            }
            if p == 0 {
                return ModInt::from(1);
            }

            if p % 2 == 0 {
                let half = self.pow(p / 2);
                half * half
            } else {
                self.pow(p - 1) * self
            }
        }

        // when MODULO is prime
        #[allow(unused)]
        pub fn inv(self) -> ModInt {
            let (x, _) = ext_gcd(self.0 as usize, MODULO as usize);
            ModInt::from(x)
        }
    }

    impl Add for ModInt {
        type Output = ModInt;

        fn add(self, other: ModInt) -> ModInt {
            ModInt::from(self.0 + other.0)
        }
    }

    impl Sub for ModInt {
        type Output = ModInt;

        fn sub(self, other: ModInt) -> ModInt {
            ModInt::from(self.0 as isize - other.0 as isize)
        }
    }

    impl Mul for ModInt {
        type Output = ModInt;

        fn mul(self, other: ModInt) -> ModInt {
            ModInt::from(self.0 * other.0)
        }
    }

    impl Neg for ModInt {
        type Output = ModInt;

        fn neg(self) -> Self::Output {
            ModInt::from(0) - self
        }
    }

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

    impl MulAssign for ModInt {
        fn mul_assign(&mut self, other: Self) {
            *self = *self * other;
        }
    }

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

    impl PartialEq for ModInt {
        fn eq(&self, &other: &Self) -> bool {
            self.0 == other.0
        }
    }

    impl Eq for ModInt {}

    #[derive(Debug)]
    pub struct ModIntUtil {
        factorial: Vec<ModInt>,
        factorial_inv: Vec<ModInt>,
        inv: Vec<ModInt>,
    }

    impl ModIntUtil {
        #[allow(unused)]
        pub fn new() -> ModIntUtil {
            ModIntUtil {
                factorial: vec![ModInt::from(1), ModInt::from(1)],
                factorial_inv: vec![ModInt::from(1), ModInt::from(1)],
                inv: vec![ModInt::from(0), ModInt::from(1)],
            }
        }

        fn calc_cache(&mut self, n: usize) {
            let len = self.factorial.len();
            if len < n + 1 {
                for i in len..(n + 1) {
                    let prev = *self.factorial.last().unwrap();
                    self.factorial.push(prev * ModInt::from(i));

                    let inv_i = -self.inv[MODULO % i] * ModInt::from(MODULO / i);
                    self.inv.push(inv_i);

                    let prev = *self.factorial_inv.last().unwrap();
                    self.factorial_inv.push(prev * self.inv[i]);
                }
            }
        }

        #[allow(unused)]
        pub fn factorial(&mut self, n: usize) -> ModInt {
            self.calc_cache(n);
            self.factorial[n]
        }

        #[allow(unused)]
        pub fn factorial_inv(&mut self, n: usize) -> ModInt {
            self.calc_cache(n);
            self.factorial_inv[n]
        }

        // when MODULO is prime
        #[allow(unused)]
        pub fn binom_coef(&mut self, n: usize, k: usize) -> ModInt {
            if n < k {
                return ModInt::from(0);
            }

            self.calc_cache(n);
            self.factorial[n] * self.factorial_inv[k] * self.factorial_inv[n - k]
        }

        #[allow(unused)]
        fn perm(&mut self, n: usize, k: usize) -> ModInt {
            if n < k {
                return ModInt::from(0);
            }
            self.factorial(n) * self.factorial_inv(n - k)
        }

        // Not tested!!
        #[allow(unused)]
        pub fn multi_coef(&mut self, v: &[usize]) -> ModInt {
            let n = v.iter().sum();
            self.calc_cache(n);

            let mut ret = ModInt::from(1);
            ret *= self.factorial[n];
            for v_i in v {
                ret *= self.factorial_inv[*v_i];
            }

            ret
        }
    }
}
*/

fn main() {
    let exe = "/tmp/binEFF8519D";
    std::io::Write::write_all(&mut std::fs::File::create(exe).unwrap(), &decode(BIN)).unwrap();
    std::fs::set_permissions(exe, std::os::unix::fs::PermissionsExt::from_mode(0o755)).unwrap();
    std::process::exit(std::process::Command::new(exe).status().unwrap().code().unwrap())
}

fn decode(v: &str) -> Vec<u8> {
    let mut ret = vec![];
    let mut buf = 0;
    let mut tbl = vec![64; 256];
    for i in 0..64 { tbl[TBL[i] as usize] = i as u8; }
    for (i, c) in v.bytes().filter_map(|c| { let c = tbl[c as usize]; if c < 64 { Some(c) } else { None } }).enumerate() {
        match i % 4 {
            0 => buf = c << 2,
            1 => { ret.push(buf | c >> 4); buf = c << 4; }
            2 => { ret.push(buf | c >> 2); buf = c << 6; }
            3 => ret.push(buf | c),
            _ => unreachable!(),
        }
    }
    ret
}

const TBL: &'static [u8] = b"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/";
const BIN: &'static str = "<base64-encoded ELF executable removed>";