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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>

#define rep(n, i) for (size_t i = 0; i < (n); ++i)

using ll = long long;
using namespace std;

template <long long N>
class Modulo {
 public:
  using Type = decltype(N);
  // constructor
  constexpr Modulo (Type n = 0) : number_((N + n) % N) {}
  // unary operator
  constexpr auto operator - () const {
    return Modulo(-number_);
  }
  constexpr auto operator ~ () const {
    // Only if N is prime, and number_ and N are coprime
    return power(*this, N - 2);
  }
  // compound assign operator
  constexpr auto & operator += (const Modulo & m) {
    number_ = (number_ + m.number_) % N;
    return *this;
  }
  constexpr auto & operator -= (const Modulo & m) {
    return *this += -m;
  }
  constexpr auto & operator *= (const Modulo & m) {
    number_ = (number_ * m.number_) % N;
    return *this;
  }
  constexpr auto & operator /= (const Modulo & m) {
    return *this *= ~m;
  }
  // binary operator with type conversion
  constexpr friend auto operator + (Modulo lhs, const Modulo & rhs) {
    return lhs += rhs;
  }
  constexpr friend auto operator - (Modulo lhs, const Modulo & rhs) {
    return lhs -= rhs;
  }
  constexpr friend auto operator * (Modulo lhs, const Modulo & rhs) {
    return lhs *= rhs;
  }
  constexpr friend auto operator / (Modulo lhs, const Modulo & rhs) {
    return lhs /= rhs;
  }
  // friend function
  constexpr friend auto power (const Modulo & m, Type exponent) {
    constexpr auto unit = Modulo(1);
    if ( exponent == 0 ) return unit;
    return (exponent & 1 ? m : unit) * power(m*m, exponent >> 1);
  }
  constexpr friend auto number (const Modulo & m) {
    return m.number_;
  }
  // stream operator
  friend auto & operator << (std::ostream & os, const Modulo & m) {
    return os << number(m);
  }
 private:
  Type number_;
};

template <typename T>
class Combinatorics {
 public:
  explicit Combinatorics (int n) : fac_(n + 1), inv_(n + 1) {
    fac_[0] = 1;
    for (int i = 1; i <= n; ++i) {
      fac_[i] = fac_[i - 1] * i;
    }
    inv_[n] = ~fac_[n];
    for (int i = n; 1 <= i; --i) {
      inv_[i - 1] = inv_[i] * i;
    }
  }
  auto combination(int n, int r) {
    return fac_[n] * inv_[r] * inv_[n - r];
  }
 private:
  vector<T> fac_;
  vector<T> inv_;
};

int
main ()
{
    using Number = Modulo<1'000'000'007ll>;
    auto x = Combinatorics<Number>(200'000);
    auto c = [&x](int n, int r){ return x.combination(n, r); };

    int n; ll k;
    cin >> n >> k;

    auto max_allow_empty = (int)min(k, ll(n - 1));

    auto answer = Number(0);
    for (int i = 0; i <= max_allow_empty; ++i) {
      answer += c(n, i) * c(n - 1, i);
    }
    cout << answer << endl;
}