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 Go (1.14.1) (judge verdict: Accepted)

package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

var sc = bufio.NewScanner(os.Stdin)

func Scanner() string {
	sc.Scan()
	return sc.Text()
}

func intScanner() int {
	n, _ := strconv.Atoi(Scanner())
	return n
}

func floatScanner() float64 {
	n, _ := strconv.ParseFloat(Scanner(), 64)
	return n
}
func stringToInt(s string) int {
	n, _ := strconv.Atoi(s)
	return n
}
func stringSliceScanner(n int) []string {
	a := make([]string, n)
	for i := 0; i < n; i++ {
		a[i] = Scanner()
	}
	return a
}
func intSliceScanner(n int) []int {
	a := make([]int, n)
	for i := 0; i < n; i++ {
		a[i] = intScanner()
	}
	return a
}
func larger(a, b int) int {
	if a < b {
		return b
	} else {
		return a
	}
}
func smaller(a, b int) int {
	if a > b {
		return b
	} else {
		return a
	}
}
func max(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x < a[i] {
			x = a[i]
		}
	}
	return x
}
func min(a []int) int {
	x := a[0]
	for i := 0; i < len(a); i++ {
		if x > a[i] {
			x = a[i]
		}
	}
	return x
}
func abs(x int) int {
	if x < 0 {
		x = -x
	}
	return x
}

var mod int
var t float64

func main() {
	mod = 1000000007
	buf := make([]byte, 0)
	sc.Buffer(buf, mod)
	sc.Split(bufio.ScanWords)
	n := intScanner()
	k := smaller(intScanner()+1, n)
	f := make([]int, n+1)
	inv := make([]int, n+1)
	f[0], inv[0] = 1, 1
	for i := 1; i < n+1; i++ {
		f[i] = f[i-1] * i % mod
		inv[i] = modinv(f[i], mod)
	}
	ans := 0
	for i := 0; i < k; i++ {
		x := f[n-1] * inv[n-i-1] % mod * inv[i] % mod
		y := f[n] * inv[i] % mod * inv[n-i] % mod
		ans += x * y % mod
		ans %= mod
	}
	fmt.Println(ans)
}
func modinv(a, m int) int {
	b, u, v := m, 1, 0
	for {
		t := a / b
		a -= t * b
		u -= t * v
		a, b, u, v = b, a, v, u
		if b == 0 {
			break
		}
	}
	u %= m
	if u < 0 {
		u += m
	}
	return u
}