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 ss second
#define ff first
#define N 200005
#define ll long long
#define mod 1000000007
#define pb push_back
#define inf 1000000009
#define mid(a,b) (a+b)/2
#define pii pair<int,int>

using namespace std;

ll n,k;
ll ans,fact[2 * N];

ll der(ll a,ll b){
	if(b == 0) return 1;
	ll x = der(a,b / 2);
	if(b % 2) return (((x * x) % mod) * a) % mod;
	return (x * x) % mod;
}

ll C(ll n,ll k){
	return (fact[n] * der((fact[n - k] * fact[k]) % mod,mod - 2)) % mod;
}

ll num(ll n,ll k){
	k -= n;
	return C(n + k - 1,k);
}

int main()
{
	scanf("%lld%lld",&n,&k);
	fact[0] = 1;
	for(int i = 1;i <= n + min(n,k);i++)
		fact[i] = (fact[i - 1] * i) % mod;
	for(int i = 1;i <= min(k,n);i++){
		ans += (C(n,i) * num(n - i,n)) % mod;
		ans %= mod;
	}
	printf("%lld",ans + 1);
}