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 PHP (7.4.4) (judge verdict: Accepted)

<?php
const MOD = 10 ** 9 + 7;
list($n, $k) = ints();
$ans = 0;
init($n);
for ($i = 0; $i <= min($k, $n - 1); ++$i)
    $ans = modAdd($ans, modMul(nCr2($n, $i), nCr2($n - 1, $n - $i - 1)));
echo $ans;
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}
// 足し算
function modAdd($x, $y)
{
    return ($x + $y) % MOD;
}

// SUM
function modSum(...$xs)
{
    $res = 0;
    foreach ($xs as $x) $res = modAdd($res, $x);
    return $res;
}

// 引き算
function modSub($x, $y)
{
    return ($x + MOD - $y) % MOD;
}

// 掛け算
function modMul($x, $y)
{
    return ($x * $y) % MOD;
}

// PRODUCT
function modProd(...$xs)
{
    $res = 1;
    foreach ($xs as $x) $res = modMul($res, $x);
    return $res;
}

// 割り算
function modDiv($x, $y)
{
    return modMul($x, modPow($y, MOD - 2));
}

// 累乗（繰り返し二乗法）
function modPow($n, $x)
{
    if ($x === 0) return 1;
    $res = (modPow($n, $x >> 1) ** 2) % MOD;
    if ($x % 2 === 1) $res = modMul($res, $n);
    return $res;
}

// 階乗
function modFac($n)
{
    if ($n === 0) return 1;
    return modMul($n, modFac($n - 1));
}

// 順列
function nPr($n, $r)
{
    if ($r === 0) return 1;
    return modMul(nPr($n, $r - 1), $n - $r + 1);
}

// 組み合わせ
function nCr($n, $r)
{
    $r = min($r, $n - $r);
    if ($r === 0) return 1;
    return modDiv(nPr($n, $r), modFac($r));
}

// 階乗、逆元を前処理
function init($n)
{
    global $fact, $ifact;
    $fact[0] = 1;
    for ($i = 1; $i <= $n; ++$i) $fact[$i] = modMul($fact[$i - 1], $i);
    $ifact[$n] = modDiv(1, $fact[$n]);
    for ($i = $n; $i >= 1; --$i)
        $ifact[$i - 1] = modMul($ifact[$i], $i);
}

// 順列（前処理）
function nPr2($n, $r)
{
    global $fact, $ifact;
    return modMul($fact[$n], $ifact[$n - $r]);
}

// 組み合わせ（前処理）
function nCr2($n, $r)
{
    global $fact, $ifact;
    return modMul(modMul($fact[$n], $ifact[$r]), $ifact[$n - $r]);
}