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 <algorithm>
#include <cstdint>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;
#define REP(i, n) for (int i = 0; i < n; i++)
#define FOR(i, s, t) for (int i = s; i < t; i++)
#define ALL(obj) obj.begin(), obj.end()

const int iINF = 1e9;
const long long llINF = 1e18;
const int MOD = 1e9 + 7;
template <class T>
inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return 1;
    }
    return 0;
}
template <class T>
inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return 1;
    }
    return 0;
}

template <int MOD>
struct ModInt {
    long long val;
    constexpr ModInt(long long v = 0) noexcept : val(v % MOD) {
        if (val < 0) val += MOD;
    }
    constexpr int getmod() { return MOD; }
    constexpr ModInt operator-() const noexcept { return val ? MOD - val : 0; }
    constexpr ModInt operator+(const ModInt& r) const noexcept { return ModInt(*this) += r; }
    constexpr ModInt operator-(const ModInt& r) const noexcept { return ModInt(*this) -= r; }
    constexpr ModInt operator*(const ModInt& r) const noexcept { return ModInt(*this) *= r; }
    constexpr ModInt operator/(const ModInt& r) const noexcept { return ModInt(*this) /= r; }
    constexpr ModInt& operator+=(const ModInt& r) noexcept {
        val += r.val;
        if (val >= MOD) val -= MOD;
        return *this;
    }
    constexpr ModInt& operator-=(const ModInt& r) noexcept {
        val -= r.val;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr ModInt& operator*=(const ModInt& r) noexcept {
        val = val * r.val % MOD;
        return *this;
    }
    constexpr ModInt& operator/=(const ModInt& r) noexcept {
        long long a = r.val, b = MOD, u = 1, v = 0;
        while (b) {
            long long t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        val = val * u % MOD;
        if (val < 0) val += MOD;
        return *this;
    }
    constexpr bool operator==(const ModInt& r) const noexcept { return this->val == r.val; }
    constexpr bool operator!=(const ModInt& r) const noexcept { return this->val != r.val; }
    friend constexpr ostream& operator<<(ostream& os, const ModInt<MOD>& x) noexcept { return os << x.val; }

    friend constexpr istream& operator>>(istream& is, ModInt<MOD>& x) noexcept { return is >> x.val; }
    friend constexpr ModInt<MOD> modpow(const ModInt<MOD>& a, long long n) noexcept {
        if (n == 0) return 1;
        auto t = modpow(a, n / 2);
        t = t * t;
        if (n & 1) t = t * a;
        return t;
    }
};

using mint = ModInt<MOD>;

long long modPow(long long x, long long n, long long mod) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * x % mod;
        x = x * x % mod;
        n >>= 1;
    }
    return res;
}

long long extGCD(long long a, long long b, long long& x, long long& y) {
    if (b == 0) {
        x = 1;
        y = 0;
        return a;
    }

    long long d = extGCD(b, a % b, y, x);
    y -= a / b * x;
    return d;
}

long long gcd(long long a, long long b) {
    if (b == 0) {
        return a;
    } else {
        return gcd(b, a % b);
    }
}

long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }

template <typename T>
map<T, int> compress(vector<T> x) {
    map<T, int> res;
    sort(x.begin(), x.end());
    x.erase(unique(x.begin(), x.end()), x.end());
    for (int i = 0; i < x.size(); i++) {
        res[x[i]] = i;
    }

    return res;
}

const int MAX = 300000;
vector<long long> fac(MAX + 1), inverseFac(MAX + 1);

long long modPow(long long x, long long n) {
    long long res = 1;
    while (n > 0) {
        if (n & 1) res = res * x % MOD;
        x = x * x % MOD;
        n >>= 1;
    }
    return res;
}

long long comb(long long a, long long b) {
    if (a == 0 && b == 0) return 1;
    if (a < b || a < 0) return 0;
    long long tmp = inverseFac[a - b] * inverseFac[b] % MOD;
    return tmp * fac[a] % MOD;
}

long long perm(long long a, long long b) {
    if (a < b) return 0;
    long long tmp = inverseFac[a - b] % MOD;
    return tmp * fac[a] % MOD;
}

long long dupc(long long a, long long b) {
    if (a == 0 && b == 0) return 1;
    if (a < 0 || b == 0) return 0;
    long long tmp = inverseFac[a - 1] * inverseFac[b] % MOD;
    return tmp * fac[a + b - 1] % MOD;
}

void init() {
    fac[0] = 1;
    inverseFac[0] = 1;
    for (long long i = 0; i < MAX; i++) {
        fac[i + 1] = fac[i] * (i + 1) % MOD;
        inverseFac[i + 1] = inverseFac[i] * modPow(i + 1, MOD - 2) % MOD;
    }
}

template <typename T>
using Vec = vector<T>;
template <typename T>
using VVec = vector<vector<T>>;
using LL = long long;
int main() {
    int N, K;
    cin >> N >> K;
    init();
    mint ans = 1;
    for (int i = 1; i < min(N, K + 1); i++) {
        ans += comb(N, i) * dupc(N - i, i);
    }
    cout << ans << endl;
    return 0;
}