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).

Examples

Input

3 2


Output

10


Input

200000 1000000000


Output

607923868


Input

15 6


Output

22583772
#include <bits/stdc++.h>
using namespace std;
using ll = long long;

constexpr int MAX_N = (1<<20);
constexpr int MOD = 1e9+7;
ll n,k;

ll f[MAX_N], invf[MAX_N];

ll modpow(ll x, ll y)
{
	ll res = 1;
	while(y > 0){
		if(y&1) res = (res * x)%MOD;
		x = x*x%MOD;
		y>>=1;
	}
	return res;
}

void init()
{
	f[0]=1;
	for(int i=1;i<=n;++i) f[i]=f[i-1]*i%MOD;
	invf[n]=modpow(f[n],MOD-2);
	for(int i=n-1;i>=0;--i) invf[i]=invf[i+1]*(i+1)%MOD;
}

ll nCk(int N, int K)
{
	if(K > N || K < 0) return 0;
	return (f[N]*invf[N-K])%MOD*invf[K]%MOD;
}

void solve()
{
	init();
	ll res = 0;
	const int L = min(n-1, k);
	for(int i=0;i<=L;++i){
		// distributing i into N-i rooms
		res = (res + nCk(n,i)*nCk(n-i-1+i,i)) % MOD; 
	}
	cout << res;
}

int main()
{
	cin >> n >> k;
	solve();
	return 0;
}