Problem:
Score : 500 points

Problem Statement

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).

Sample Input 1

3 2

Sample Output 1

10

Let c_1, c_2, and c_3 be the number of people in Room 1, 2, and 3 now, respectively. There are 10 possible combination of (c_1, c_2, c_3):

(0, 0, 3)

(0, 1, 2)

(0, 2, 1)

(0, 3, 0)

(1, 0, 2)

(1, 1, 1)

(1, 2, 0)

(2, 0, 1)

(2, 1, 0)

(3, 0, 0)

For example, (c_1, c_2, c_3) will be (0, 1, 2) if the person in Room 1 goes to Room 2 and then one of the persons in Room 2 goes to Room 3.

Sample Input 2

200000 1000000000

Sample Output 2

607923868

Print the count modulo (10^9 + 7).

Sample Input 3

15 6

Sample Output 3

22583772

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <iostream>
#include <array>
#include <algorithm>
#include <vector>
#include <bitset>
#include <set>
#include <unordered_set>
#include <cmath>
#include <complex>
#include <deque>
#include <iterator>
#include <numeric>
#include <map>
#include <unordered_map>
#include <queue>
#include <stack>
#include <string>
#include <tuple>
#include <utility>
#include <limits>
#include <iomanip>
#include <functional>
#include <cassert>
using namespace std;

using ll=long long;
template<class T> using V = vector<T>;
template<class T, class U> using P = pair<T, U>;
using vll = V<ll>;
using vvll = V<vll>;
#define rep(i, k, n) for (ll i=k; i<(ll)n; ++i)
#define REP(i, n) rep(i, 0, n)
#define ALL(v) v.begin(),v.end()
template < class T > inline bool chmax(T& a, T b) {if (a < b) { a=b; return true; } return false; }
template < class T > inline bool chmin(T& a, T b) {if (a > b) { a=b; return true; } return false; }
#define DEBUG_VLL(vec) REP(sz, vec.size()) std::cerr<<vec[sz]<<(sz==vec.size()-1?'\n':' ');

const long long MOD = 1000000007;
const long long HIGHINF = (long long)1e18;
const int INF = (int)1e9;

const ll MAX = 400005;

vector<long long> fac(MAX, 0), finv(MAX, 0), inv(MAX, 0);

void initCombTable() {
    fac.at(0) = 1; fac.at(1) = 1;
    finv.at(0) = 1; finv.at(1) = 1;
    inv.at(1) = 1;
    for (ll i = 2; i < MAX; i++) {
        fac.at(i) = fac.at(i-1) * i % MOD;
        inv.at(i) = MOD - inv.at(MOD%i) * (MOD / i) % MOD;
        finv.at(i) = finv.at(i-1) * inv.at(i) % MOD;
    }
}

long long nCk(long long n, long long k) {
    if (n < 0 || k < 0 || n < k) return 0;
    return fac.at(n) * (finv.at(k) * finv.at(n-k) % MOD) % MOD;
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    ll n, k; cin >> n >> k;
    initCombTable();
    if (k >= n - 1) {
        ll ans = nCk(2 * n - 1, n - 1);
        cout << ans << '\n';
    } else {
        ll ans = 0;
        for (ll i = 0; i <= k; i++) {
            (ans += nCk(n, i) * nCk(n - 1, i) % MOD) %= MOD;
        }
        cout << ans << '\n';
    }
    return 0;
}