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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (N, K) = readLine()!!.split(" ").map(String::toInt)
    val k = Math.min(K, N-1)
    val combi = Combination(N)
    var sum = MInt(0)
    for (i in 0..k) {
        sum = sum + combi(N, i) * combi(N - 1, i)
    }
    println(sum)
}

class MInt {
    private val MOD = 1000000007L
    var v: Long

    constructor(v: Long) {
        this.v = v % MOD
    }

    constructor(v: Int) {
        this.v = v.toLong() % MOD
    }

    operator fun plus(b: MInt): MInt {
        val a = MInt(v)
        a += b
        return a
    }

    operator fun minus(b: MInt): MInt {
        val a = MInt(v)
        a -= b
        return a
    }

    operator fun times(b: MInt): MInt {
        val a = MInt(v)
        a *= b
        return a
    }

    operator fun div(b: MInt): MInt {
        val a = MInt(v)
        a /= b
        return a
    }

    operator fun plusAssign(b: MInt) {
        v += b.v
        if (v >= MOD) v -= MOD
    }

    operator fun minusAssign(b: MInt) {
        v -= b.v
        if (v < 0) v += MOD
    }

    operator fun timesAssign(b: MInt) {
        v *= b.v
        v %= MOD
    }

    operator fun divAssign(b: MInt) {
        this *= b.inv()
    }

    fun inv(): MInt {
        var a = v
        var b = MOD
        var u = 1L
        var w = 0L
        while (b != 0L) {
            val t = a / b
            a -= t * b
            u -= t * w
            var tmp = a
            a = b
            b = tmp
            tmp = u
            u = w
            w = tmp
        }
        u %= MOD
        if (u < 0) u += MOD
        return MInt(u)
    }

    fun pow(N: Long): MInt {
        var ans = MInt(1)
        var a = this
        var n = N
        while (n > 0) {
            if (n.and(1) == 1L) {
                ans = ans * a
            }
            a = a * a
            n = n.shr(1)
        }
        return ans
    }

    override fun toString(): String {
        return v.toString()
    }
}

class Combination(n: Int) {
    private val fact = arrayOfNulls<MInt>(n + 1)
    private val ifact = arrayOfNulls<MInt>(n + 1)

    init {
        fact[0] = MInt(1)
        (1..n).forEach { i -> fact[i] = fact[i - 1]!! * MInt(i) }
        ifact[n] = fact[n]!!.inv()
        (n downTo 1).forEach { i -> ifact[i - 1] = ifact[i]!! * MInt(i) }
    }

    operator fun invoke(n: Int, k: Int): MInt {
        if (k < 0 || n < k) return MInt(0)
        return (fact[n]!! * ifact[k]!! * ifact[n - k]!!)
    }
}