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
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.Scanner;

public class Main {
    private long fac[];
    private long finv[];
    private long inv[];
    private static int MAX_LEN = 510000;
    private static int MOD = 1000000007;
    public static void main(String[] args) {
        Main main = new Main();
        main.COMinit();
        main.solve();
    }

    public void solve() {
        Scanner scan = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
        int N = scan.nextInt();
        int K = scan.nextInt();
        long ans = 0;
        for (int i = 0; i <= Math.min(N,K); i++) {
            long t1 = COM(N, i);
            // N-i個に1以上を配置して和をnにする
            // N-i個に0以上を配置して和をn-(n-i)=iにする
            long t2 = COM(i+(N-i-1),i);
            ans += t1 * t2;
            ans %= MOD;
        }
        System.out.println(ans);
    }
    void COMinit() {
        this.fac = new long[MAX_LEN];
        this.finv = new long[MAX_LEN];
        this.inv = new long[MAX_LEN];
        this.fac[0] = this.fac[1] = 1;
        this.finv[0] = this.finv[1] = 1;
        this.inv[1] = 1;
        for (int i = 2; i < MAX_LEN; i++) {
            fac[i] = fac[i-1] * i % MOD;
            inv[i] = MOD - inv[MOD%i] * (MOD / i) % MOD;
            finv[i] = finv[i-1] * inv[i] % MOD;
        }
    }
    long COM(int n, int k) {
        if (n < k) {
            return 0;
        };
        if (n <0 || k < 0) {
            return 0;
        }
        return fac[n] * (finv[k] * finv[n - k]%MOD)%MOD;
    }
}
