func main()
	const mod: int :: 1000000007
	var a: int :: cui@inputInt()
	var b: int :: cui@inputInt()
	var n: int :: cui@inputInt()
	var ans: int :: 1
	for gcd(a, b)
		do dfs(&ans, gcd, a, b, n, 1)
	end for
	do cui@print("\{ans}\n")
	
	func dfs(ans: &int, gcd: int, a: int, b: int, n: int, depth: int)
		if(depth = n)
			do ans :* gcd
			do ans :% mod
			ret
		end if
		for i(a, b)
			do dfs(&ans, math@gcd(gcd, i), a, b, n, depth + 1)
		end for
	end func
end func