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 Lua (5.3.2) (judge verdict: Accepted)

local read = setmetatable({}, {__index = function(t, k) local a = {} for i=1,#k do table.insert(a, '*'..string.sub(k, i, i)) end local r = io.read local u = table.unpack or unpack return function() return r(u(a)) end end})
read.N = function(N) local t={} for i=1,N do t[i]=read.n() end return t end
string.totable = function(s) local t={} local u=string.sub for i=1,#s do t[i] = u(s, i, i) end return t end
string.split = function(s) local t={} for w in string.gmatch(s, "[^%s]+") do table.insert(t, w) end return (table.unpack or unpack)(t) end
local function array(dimension, default_val) local n=dimension local m={}if default_val~=nil then m[1]={__index=function()return default_val end}end for i=2,n do m[i]={__index=function(p, k)local c=setmetatable({},m[i-1])rawset(p,k,c)return c end}end return setmetatable({},m[n])end
----
local floor = math.floor
local MOD = floor(10^9)+7


-- returns (b^n) % m
local function modpow(b, n, m)
    if n == 0 then
        return 1
    elseif n % 2 == 0 then
        -- be careful about overflow of b*b
        return modpow(b * b % m, n//2, m)
    else
        return b * modpow(b, n - 1, m) % m
    end
end

-- returns n! % m
local function modfactorial(n, m)
    local a = 1
    for i=1, n do
        a = a * i % m
    end
    return a
end

local function make_mod_nCr(nmax, m)
    -- Create n! table
    local mfac = {}
    mfac[0] = 1
    for i=1,nmax do
        mfac[i] = mfac[i-1] * i % m
    end
    -- Create (n!)^(-1) table
    -- (n!)^(-1) ≡ (n!)^(m - 2)  <mod m>
    local invmfac = {}
    invmfac[nmax] = modpow(mfac[nmax], m - 2, m)
    for i=nmax,1,-1 do
        -- ((a-1)!)^(-1) ≡ a * (a!)^(-1)  <mod m>
        invmfac[i-1] = i * invmfac[i] % m
    end
    -- returns nCr % m
    local function mod_nCr(n, r)
        -- nCr ≡ n! * (r!)^(-1) * ((n-r)!)^(-1)  <mod m>
        local a = mfac[n] * invmfac[r] % m
        a = a * invmfac[n-r] % m
        return a
    end
    return mod_nCr
end

-- larger n and small r
local function make_mod_nCr_2(rmax, m)
    -- Create n! table
    local mfac = {}
    mfac[0] = 1
    for i=1,rmax do
        mfac[i] = mfac[i-1] * i % m
    end
    -- Create (n!)^(-1) table
    -- (n!)^(-1) ≡ (n!)^(m - 2)  <mod m>
    local invmfac = {}
    invmfac[rmax] = modpow(mfac[rmax], m - 2, m)
    for i=rmax,1,-1 do
        -- ((a-1)!)^(-1) ≡ a * (a!)^(-1)  <mod m>
        invmfac[i-1] = i * invmfac[i] % m
    end
    -- partial factory ()
    local pmfac
    -- returns nCr % m
    local function mod_nCr(n, r)
        if r > n then
            return 0
        end
        if r > n/2 then
            r = n - r
        end
        -- nCr ≡ (n * (n - 1) * ... * (n-r+1)) * (r!)^(-1)  <mod m>
        local a = 1
        for i=n, n-r+1, -1 do
            a = (a * i) % m
        end
        a = a * invmfac[r] % m
        return a
    end
    return mod_nCr
end


----
local n, k = read.nn()

local nCr = make_mod_nCr(n, MOD)

local ans = 0
for i=0,math.min(n-1,k) do
    local empty_room_pattern = nCr(n, i)
    local nonempty_room_pattern = nCr(n-1, i)
    ans = (ans + (empty_room_pattern * nonempty_room_pattern % MOD)) % MOD
end

print(ans)