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>
#define pb push_back
#define mkp make_pair
using namespace std;
typedef long long ll;
const ll mod=1e9+7;
const int maxn=2e5+5;
const int inf=0x3f3f3f3f;
ll fac[maxn];
ll mul(ll a,ll b){
	return ((a%mod)*(b%mod)+mod)%mod;
}
void pre_fac(int up){
	fac[0]=fac[1]=1;
	for(int i=2;i<up;i++)fac[i]=mul(fac[i-1],i);
}
ll fpow(ll a,ll b){
	ll ans=1;
	while(b){
		if(b&1)ans=mul(ans,a);
		a=mul(a,a);
		b>>=1;
	}
	return ans;
}
ll inv(ll x){
	return fpow(x,mod-2);
}
ll C(ll n,ll m){
	return mul(inv(fac[n-m]),mul(fac[n],inv(fac[m])));
}
ll add(ll a,ll b){
	return (a+b+mod)%mod;
}
int main(){
	ll n,k;
	pre_fac(2e5+1);
	cin>>n>>k;
	k=min(k,n-1);
	ll ans=0;
	for(int i=0;i<=k;i++){
		ans=add(ans,mul(C(n,i),C(n-i+i-1,i)));
	}
	cout<<ans<<endl;
	return 0;
}
