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 Common Lisp (SBCL 1.1.14) (judge verdict: Accepted)

#-swank
(unless (member :child-sbcl *features*)
  (quit
    :unix-status
    (process-exit-code
      (run-program *runtime-pathname*
                   `("--control-stack-size" "128MB"
                     "--noinform" "--disable-ldb" "--lose-on-corruption" "--end-runtime-options"
                     "--eval" "(push :child-sbcl *features*)"
                     "--script" ,(namestring *load-pathname*))
                   :output t :error t :input t))))


(defun split (x str)
  (let ((pos (search x str))
        (size (length x)))
    (if pos
      (cons (subseq str 0 pos)
            (split x (subseq str (+ pos size))))
      (list str))))

(defparameter *factorial-dp* (make-array 400001 :initial-element nil))
(defparameter *factorial-inv-dp* (make-array 400001 :initial-element nil))

(defparameter *mod* (+ (expt 10 9) 7))

(defun factorial (x)
  (if (<= x 1) 1
    (if (aref *factorial-dp* x)
      (aref *factorial-dp* x)
      (setf (aref *factorial-dp* x) (mod* x (factorial (1- x)))))))

(defun mod+ (&rest body)
  (reduce (lambda (a b) (mod (+ a b) *mod*)) body))
(defun mod- (&rest body)
  (reduce (lambda (a b) (mod (- a b) *mod*)) body))
(defun mod* (&rest body)
  (reduce (lambda (a b) (mod (* a b) *mod*)) body))
(defun modpow (x y)
  (if (zerop y) 1
    (mod* (if (oddp y) x 1)
          (modpow (mod* x x) (ash y -1)))))

(defun factorial-inv (x)
  (let ((res (aref *factorial-inv-dp* x)))
    (if res
      res
      (setf (aref *factorial-inv-dp* x) (modinv (factorial x))))))


(defun modinv (x)
  (modpow x (- *mod* 2)))

(defun mod/ (&rest body)
  (reduce (lambda (a b) (mod* a (modinv b))) body))

(defun combination (a b)
  (mod* (factorial a) (factorial-inv b) (factorial-inv (- a b))))


(factorial-inv 400000)
(loop for i downfrom 400000 to 1
      do
      (setf (aref *factorial-inv-dp* (1- i))
            (mod* (aref *factorial-inv-dp* i) i)))

(let* ((n (read))
       (k (read))
       (ans (combination (1- (* n 2)) n)))
  (loop for zeros from (1+ k) below n
        do
        (setf ans (mod- ans 
                        (mod* 
                          (combination n zeros) 
                          (combination (1- n) (- n zeros 1))))))
  (princ ans))