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;

typedef long long ll;

const ll mod=1e9+7;
const ll maxn=2e5+5;


ll inv[maxn];
void getInv(){
	inv[1]=1;
	for(ll i=2;i<maxn;i++){
		inv[i]=(mod-mod/i)*inv[mod%i]%mod;
	}
}

ll qPow(ll a,ll b){
	ll ans=1;
	while(b){
		if(b&1) ans=(ans*a)%mod;
		a=(a*a)%mod;
		b>>=1;
	}
	return ans;
}

ll C(ll x,ll y){
	ll ans=1;
	for(int i=0;i<y;i++)
	{
		ans=(ans*(x-i)%mod*inv[i+1])%mod;
	}
	return ans;
}

int main(){
	getInv();
	ll n,k;
	scanf("%lld%lld",&n,&k);
	ll tmp=min(n-1,k);
	ll ans=0;ll kk=1;ll kk2=1;
	for(ll i=0;i<=tmp;i++){
		ans=(ans+kk*kk2%mod)%mod;
		kk=(kk*(n-i))%mod;
		kk=(kk*inv[i+1])%mod;
		kk2=(kk2*(n-i-1))%mod;
		kk2=(kk2*inv[i+1])%mod;
	}
	printf("%lld\n",ans);
	return 0;
}