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 <iostream>
#ifdef MBP
#include "stdc++.h"
#else
#include <bits/stdc++.h>
#endif

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

#define REP(i, n) for (long long int i = 0, i##_len = (n); i < i##_len; ++i)
#define REP_R(i, n) for (long long int i = (n - 1); i >= 0; --i)
#define ALL(x) (x).begin(), (x).end()
#define SZ(x) ((long long int)(x).size())
#define BIT(n) (1LL << (n))
#define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end());

#define DEBUG

#ifdef DEBUG
#define OUT(x) std::cout << (x) << std::endl
#define OUT2(x, y) std::cout << (x) << "," << (y) << std::endl
#define OUT3(x, y, z) std::cout << (x) << "," << (y) << "," << (z) << std::endl
#define OUTPA(p) OUT2(p.first, p.second)
#else
#define OUT(x) NULL
#define OUT2(x, y) NULL
#define OUT3(x, y, z) NULL
#define OUTPA(p) NULL
#endif

#define INF INT_MAX
#define INFLL LLONG_MAX
#define PB push_back
#define MOD 1000000007LL

#define LSB(x) __builtin_ctzll(x)
#define MSB(x) 64LL - __builtin_clzll(x) - 1LL
#define MSBINT(x) 32LL - __builtin_clz(x)
#define BITCNT(x) __builtin_popcountll(x)

using namespace std;
using uif = uint_fast64_t;
using ll = long long int;
using vec = vector<ll>;
using mat = vector<vector<ll>>;
using pa = pair<ll, ll>;
using tTree = __gnu_pbds::tree<ll, __gnu_pbds::null_type, less<ll>, __gnu_pbds::rb_tree_tag, __gnu_pbds::tree_order_statistics_node_update>;

template <class T>
inline void input(T &arr)
{
  ll n = arr.size();
  REP(i, n)
  cin >> arr[i];
}
template <class T>
inline void inputPA(T &arr)
{
  ll n = arr.size();
  REP(i, n)
  cin >> arr[i].first >> arr[i].second;
}

template <class T>
using PQ = priority_queue<T>;
template <class T>
using PQG = priority_queue<T, vector<T>, greater<T>>;

const ll dx[4] = {1, 0, -1, 0};
const ll dy[4] = {0, 1, 0, -1};
const ll dx8[8] = {1, 1, 0, -1, -1, -1, 0, 1};
const ll dy8[8] = {0, 1, 1, 1, 0, -1, -1, -1};

template <class T>
bool chmax(T &, const T &);
template <class T>
bool chmin(T &, const T &);

ll qp(ll a, ll b);
ll qp(ll a, ll b, ll mo);

ll mod_pow(ll, ll);
ll mod_add(ll, ll);
ll mod_mul(ll, ll);
ll mod_div(ll, ll);
void make_fact(ll);
void make_invfact(ll);
void init_fact();

ll combination(ll, ll);

#define FACSIZE 400002LL

ll invfac[FACSIZE];
ll fac[FACSIZE];

int main(void)
{
  ll n, k;
  cin >> n >> k;
  init_fact();

  if (k >= n - 1)
  {
    cout << combination(2 * n - 1, n) << endl;
  }
  else
  {
    ll ans = 1;
    for (ll i = 1; i <= k; i++)
    {
      ll val1 = combination(n, i);
      ll val2 = combination(n - 1, i);
      //OUT2(val1, val2);
      ll val = mod_mul(val1, val2);
      ans = mod_add(ans, val);
    }
    cout << ans << endl;
  }

  return 0;
}

template <class T>
bool chmax(T &a, const T &b)
{
  if (a < b)
  {
    a = b;
    return 1;
  }
  return 0;
}
template <class T>
bool chmin(T &a, const T &b)
{
  if (b < a)
  {
    a = b;
    return 1;
  }
  return 0;
}

ll qp(ll a, ll b)
{
  ll ans = 1LL;
  do
  {
    if (b & 1LL)
      ans = 1LL * mod_mul(ans, a) % MOD;
    a = 1LL * mod_mul(a, a) % MOD;
  } while (b >>= 1LL);
  return ans;
}
ll qp(ll a, ll b, ll mo)
{
  ll ans = 1LL;
  do
  {
    if (b & 1LL)
      ans = 1LL * (ans % mo) * (a % mo);
    a = 1LL * (a % mo) * (a % mo);
  } while (b >>= 1LL);
  return ans;
}

ll mod_pow(ll x, ll r)
{
  if (r == 0)
    return 1;
  else if (r == 1)
    return x % MOD;
  else if (r % 2 == 0)
  {
    ll t = mod_pow(x, r / 2) % MOD;
    return t * t % MOD;
  }
  else
  {
    ll t = mod_pow(x, r / 2) % MOD;
    ll k = t * t % MOD;
    return k * x % MOD;
  }
}
ll mod_add(ll a, ll b)
{
  return (a + b) % MOD;
}

ll mod_mul(ll a, ll b)
{
  return (a * b) % MOD;
}

ll mod_div(ll a, ll b)
{
  return mod_mul(a, mod_pow(b, MOD - 2));
}

void make_fact(ll n)
{
  fac[0] = 1;
  REP(i, n)
  {
    fac[i + 1] = mod_mul(fac[i], i + 1);
  }
}

void make_invfact(ll n)
{
  invfac[n] = mod_pow(fac[n], MOD - 2);
  REP_R(i, n)
  {
    invfac[i] = mod_mul(invfac[i + 1], i + 1);
  }
}

void init_fact()
{
  make_fact(FACSIZE - 1);
  make_invfact(FACSIZE - 1);
}

ll combination(ll n, ll c)
{

  return mod_mul(fac[n], mod_mul(invfac[c], invfac[n - c]));
}
///////////////fact
/*
  init_fact();
  cout << fac[5] << endl;
  cout << invfac[5] << endl;
  cout << combination(8, 4) << endl;
  cout << combination(31, 8) << endl;
  //*/
///////////////////