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: Wrong Answer)

#include <cstdio>
#include <algorithm>
#define repi(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,a) repi(i,0,a)
#define all(a) (a).begin(), (a).end()

using ll = long long;
constexpr ll mod = 1000000007;

ll n, k;

ll powMod( ll x, ll y )
{
  ll ret = 1ll;

  while( y > 0 )
  {
    if( y & 1 )
      ret = (ret * x) % mod;

    x = (x*x) % mod;

    y >>= 1;
  }

  return ret;
}

ll fact[200010], inv[200010];

ll comb( ll n, ll r )
{
  if( n < r || n <= 0 || r < 0 )
    return 0;

  return fact[n]*inv[r]%mod*inv[n-r]%mod;
}

int main()
{
  scanf( "%lld%lld", &n, &k );

  fact[0] = 1;
  rep( i, 200010 )
    fact[i+1] = (i+1)*fact[i]%mod;

  rep( i, 200010 )
    inv[i] = powMod( fact[i], mod-2 );

  ll ans = 0;

  repi( r, 0, std::min(n-1,k)+1 )
    ans = (ans+comb(n,r)*comb(n-1,r)%mod)%mod;

  printf( "%lld\n", ans );

  return 0;
}