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;
#define ll long long
const ll mod=1e9+7;
ll fac[500005],inv[500005];
const int N=500000;
ll power(ll base,ll n)
{
    ll r=1;
    while(n)
    {
        if(n&1) r=(r*base)%mod;
        base=(base*base)%mod;
        n/=2;
    }
    return r%mod;
}

void pre()
{
    fac[0]=1;
    for(int i=1;i<=N;i++)
    {
        fac[i]=fac[i-1]*i%mod;
    }
    inv[N]=power(fac[N],mod-2);
    for(int i=N-1;i>=0;i--)
    {
        inv[i]=inv[i+1]*(i+1)%mod;
    }
}
ll C(ll m,ll n)
{
    return fac[n]*inv[m]%mod*inv[n-m]%mod;
}

int main()
{
    ios::sync_with_stdio(false);
    cin.tie(0);
    ll n,k;
   cin>>n>>k;
   pre();
   k=min(k,n-1);
   ll ans=0;
   for(int i=0;i<=k;i++)
   {
       ans+=C(i,n)*C(n-i-1,n-1)%mod;
   }
   ans%=mod;
   cout<<ans<<'\n';









}
