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 int maxn=2e5+5;
const int mod=1e9+7; 
ll f[maxn],inv[maxn];
ll quick(ll a,ll b){ 
    ll ans=1;  
    a=a%mod;
    while(b!=0){
        if(b&1) ans=(ans*a)%mod;
        b>>=1;
        a=(a*a)%mod;
    }
    return ans;
}
ll cal(int n,int k)
{
	return f[n]*inv[n-k]%mod*inv[k]%mod;
}
int main()
{
	int n,k;
	f[0]=inv[0]=1;
	for(int i=1;i<maxn;++i) f[i]=f[i-1]*i%mod,inv[i]=quick(f[i],mod-2); 
	scanf("%d %d",&n,&k);
	ll ans=0;
	for(int i=0;i<=min(n-1,k);++i) ans+=cal(n,i)*cal(n-1,i)%mod,ans%=mod;
	printf("%lld\n",ans);
}