How could I like my game to a private Github repository?

All put together

local EncodeBase64 -- from http://lua-users.org/wiki/BaseSixtyFour
do
	-- character table string
	local b='ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz0123456789+/'

	-- encoding
	function EncodeBase64(data)
		return ((data:gsub('.', function(x) 
			local r,b='',x:byte()
			for i=8,1,-1 do r=r..(b%2^i-b%2^(i-1)>0 and '1' or '0') end
			return r;
		end)..'0000'):gsub('%d%d%d?%d?%d?%d?', function(x)
			if (#x < 6) then return '' end
			local c=0
			for i=1,6 do c=c+(x:sub(i,i)=='1' and 2^(6-i) or 0) end
			return b:sub(c+1,c+1)
		end)..({ '', '==', '=' })[#data%3+1])
	end
end

local function GetWithBasicAuthAsync(username: string, token: string, url: string, nocache: boolean?, additionalHeaders: any?)
	local headers = additionalHeaders and table.clone(additionalHeaders) or {}
	local auth = EncodeBase64(username .. ":" .. token)
	headers["Authorization"] = "Basic " .. auth
	return game:GetService("HttpService"):GetAsync(url, nocache, headers)
end

local http = game:GetService("HttpService")
local user = "your_username"
local token = "b2J2aW91c2x5IHRoaXMgaXNuJ3QgbXkgdG9rZW4="
local result = GetWithBasicAuthAsync(user, token, "https://api.github.com/repos/your_username/your_repo")
print(http:JSONDecode(result))

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