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;
const long long mod=1000000007,inf=1000000007;
inline long long qpow(long long a,long long b){
	long long res=1;
	while(b){
		if(b&1)(res*=a)%=mod;
		(a*=a)%=mod;
		b>>=1;
	}
	return res;
}
long long n,k,ans=0;
inline long long inv(long long a) {return qpow(a,mod-2);}
long long f[200005];
long long c[200005];
int main(){
	cin>>n>>k;
	k=min(n,k);
	c[0]=f[0]=1;
	for(int i=1;i<=n;++i)f[i]=f[i-1]*(n-i)%mod*inv(i)%mod;
	for(int i=1;i<=n;++i)c[i]=c[i-1]*(n-i+1)%mod*inv(i)%mod;
	for(int i=0;i<=k;++i)(ans+=c[i]*f[i])%=mod;
	cout<<ans;
	return 0;
}