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 ull unsigned long long
#define ll long long
const int w=3e5+5;
const ll mod=1e9+7;
ll ni[w],fac[w];
ll quick(ll x,ll y)
{
    ll ans=1;
    while(y)
    {
        if(y&1)
            ans=ans*x%mod;
        x=x*x%mod;
        y/=2;
    }
    return ans;
}
ll C(ll n,ll m)
{
    return fac[n]*ni[m]%mod*ni[n-m]%mod;
}
int main()
{
    int i,j;
    ll n,m;
    cin>>n>>m;
    fac[0]=1,fac[1]=1;
    for(i=2;i<=n;i++)
        fac[i]=fac[i-1]*i%mod;
    ni[n]=quick(fac[n],mod-2);
    for(i=n-1;i>=0;i--)
        ni[i]=ni[i+1]*(i+1)%mod;
    m=min(m,n-1);
    ll ans=0;
    for(i=0;i<=m;i++)
        ans+=C(n,i)*C(n-1,n-i-1)%mod,ans%=mod;
    cout<<ans<<endl;
    return 0;
}
